Will forcing two magnets together along repeling poles weaken the magnets after a while?

Yes. And it is observed practically as well (A strong magnet can also demagnetize itself). Magnetic depolarization (demagnetization) or magnetization reversal is extremely relevant in engineering and something magnetic circuit designers are required to pay close attention to (specifically in magnetic storage and situations where hard magnetic materials are exposed to dynamic, alternating EM fields, ie. actuators).

You can see this happen in practical experiments by bringing large N30+ grade, rod shaped permanent magnets (PM) close to small/cheap compasses [north-seeking behavior is lost in soft ferrites], magnetic tapes and older (pre 1995) hard disk drives [data corruption]. You also see this in older brushed/brushless DC motors where demagnetization manifests as embrittled stator/rotor permanent magnets. Also see Degaussing/Deperming. However, you probably won't see this happen in similarly sized/shaped/graded permanent magnets.

This is important when designing a full hardware system, say a Hard-Disk Drive or a smartphone or any ultrathin portable PC. Such systems have multiple electromagnetic systems made of mixed grade magnetic materials. For example, the BLDCs to spin platters use hard ferrites for their magnets, the voice coil arrangements use rare earths, older magnetic R/W head used ferrite cores, newer GMR heads use a defined flux path through soft ferrites, the older magnetic platters used soft/ferric oxide material coatings [new ones use Cobalt alloys, higher coercivity films], cameras have thin [high aspect ratio/HAR] rare earth walls for autofocus voice coils, vibe motors have HAR PMs, connectors/switches/latches also use HAR NdFeB materials now. In engineering terms, a poorly nuanced flux path design will contribute to both functional and utility failure in such systems.

(These are only examples from consumer devices; I am sure there are plenty of demagnetization anecdotes from the high field medical instruments/MRI, HE Physics and analysis instrumentation segments. For example even rare earth (hard) magnetic materials fracture in the presence of high fields: Page on nature.com)

The magnetic domain description from Inna Vishik's answer is compactly quantified by the normal (extrinsic/open circuit) and intrinsic (closed circuit) BH-curves of a magnetic material. Practical engineering does not in general require considerations of domain switching, pinning or stress-induced matrix failure. So the curve provides a heuristic description and allows prediction of a material's magnetic behavior in the presence of an external field. That said, information about domain switching behavior is also implicitly described by the curve.

For a decent but incomplete textbook description of the curve, look here: K&J Magnetics Blog , Permanent Magnets

Three critical parameters obtained from the operational quadrant (the second, top-left quadrant) are the remanence/residual magnetization, the intrinsic/extrinsic coercive field strengths and the actual operational load curve (which depends on the shape/self-demagnetization and ambient EM field structure of the PM).

The act of bringing two like poles of magnets close together introduces both magnets to an external 'demagnetizing' field. If the demagnetization field is greater than the effective coercive field strength (obtained from the load-curve, equal to or lesser than the extrinsic coercive strength) the domains switch polarization (through critical percolation) catastrophically, and end up with a reverse polarization. The effective coercive field depends on the shape, volume, metallurgy and work history of the specific sample, and is different (lesser than equal to) from both the bulk intrinsic/extrinsic predictions of coercive field strength.

Note that magnetic domains are defined energetically (not mechanically, for example grain boundaries or dislocations or crystal defects/voids are geometrically/mechanically defined), so individual domain switching does not get affected by any mechanical 'pinning'. So you cannot 'pin' the domain walls to an absolute polarization in a magnetic material.

The domain walls themselves have a finite atomic thickness and width (around a few 100 atoms in each dimension, over which polarization changes continuously from one orientation to its neighboring domain's orientation). A demagnetization field moves this wall around inside the pinned region. A pinned region requires additional energy for switching between polarizations, but this does not imply an inability to do so. Pinning is a technique used to engineer materials with specific properties/coercivities by manipulating the microstructure/anisotropy to limit minimum contiguous domain sizes and by increasing the volume of wall structures.

Unlike the right-most block shown in this image, magnetic domains in actual PMs do not look perfect like that (because, polycrystalline/MMCs). They are mixed, non-aligned and unevenly distributed based on grain size/geometry even when magnetized (the domains prefer to align in a manner that leads to closed flux paths - flux closure domains, which leads to lowering the magnetostatic energy of the system). This minimal (residual) non-uniformity in magnetic domain distribution happens at saturation - to align the domains better would require higher energy and would lead to intra-granular stresses (resulting in embrittlement and subsequent failure). If they were absolutely aligned, then the BH curve would be perfectly rectangular (as shown in the image below); NdFeB magnets approach this shape; the smoothly curved knees in actual BH curves come from the mixed domain nature of real magnets. This curve is further affected by the shape of the magnet (demagnetization through easier/low-reluctance flux paths through the material)

From: Permanent Magnet Materials

This magnetic domain wall behavior and polarization switching is easily visualized in the cobalt-alloy magnetic recording layers of HDDs. Data in HDDs, in the form of 0s and 1s, is stored in a bit cell. A bit cell is physical 3D region (mostly flat, but also has a depth, see PMR) made of many grains of 10s of nanometer dimensions (every manufacturer and technology has different values; numbers in perpendicular magnetic recording/PMR tech are also different).

[A bit is a 0 when the average polarization across the bit cell remains the same across the cell, and a 1 when the polarization shows an average transition (negative to positive, or the other way round) behavior inside the cell. These bit cells are arranged in concentric tracks on the HDD platters, and include overhead for additional servo correction bit cell tracks and error-correction tracks in addition to cell-isolation tracks.]

Each grain possesses a single magnetic domain. The clump of grains in a bit cell have multiple magnetic domains, not all of them have a single, uniform polarization. When data is written - the write head applies a demagnetization field of strength greater than the coercivity of the material - the domain walls that exist inside the small clumps 'move', and 'jump' across grain boundaries to coalesce/recede. The newer Co-Ni thin film platters have higher coercivities than other older ferric oxide ones (and consequently are harder to demagnetize).

This bit cell does not have a nice uniform polarization structure either (as shown in the closeup magnetic force microscope/MFM images below). This introduces noise in the signals from the read head (and manufacturer specific ECCs).

From: Micromagnetic Microscopy and Modeling

...Images of a magnetic medium. The color images show the direction of the in-plane magnetization of a CoNi hard disk at two different magnifications. The relationship between color and direction is given by the inset color wheel. The higher magnification image clearly shows the jaggedness of the recorded transitions as well as the complex magnetic structure at the track edges. The simultaneously measured topography shown in the gray-scale image is used to correlate the medium's magnetic structure with its roughness. (Courtesy of John Unguris, Robert J. Celotta and Daniel T. Pierce, National Institute of Standards and Technology.)

From: Asylum Research AFM News

Five frames showing a piece of PMR hard disk degaussed with an in-plane ~0.5 Tesla magnetic field ...

Let's conclude with specific examples: Classical grades of Alnicos (with strongly polar Fe-Co tubular rods pinned in a weakly polar Ni-Al matrix) have low intrinsic coercivities (~0.7 KOe) and can be easily demagnetized using any stronger PM.

Hard ferrites, remanence of 4kG/.4T, coercivity around 3KOe, or about N3 grade, can be exposed to moderate demagnetizing fields, and since they are cheap - they are the ones most commonly used in large engineering volumes motors. But these can be demagnetized

It is much more harder to demagnetize NdFeBs, but if you have really thin discs (<1 mm thickness in direction of polarization, with radii of around> 10 mm), you can. (In fact, these self demagnetize noticeably).