What will happen to a permanent magnet if we keep the same magnetic poles of two magnets close together for a long time?
If we keep two magnets with same poles together, then they'll become weaker overtime. I once deliberately did it to find out what would happen.
This could be explained with Magnetic Domain Theory. In magnets, the magnetic domains are aligned in the same direction, giving them a strong magnetic field. If two magnets are kept with like poles facing each other,
... the effect will be similar to applying an external magnetic field to the magnet in direction opposite to the magnetic field of the magnet. This will result in the magnetic domains trying to align with the external magnetic field, and in this case, as the magnetic fields of both magnets are equal, some of the domains will disorient, thus weakening the magnetic field of each magnet,
In my experience (with ferroxcube materials) nothing happens. In fact, to change the magnetic properties the magnetic domains inside must be reoriented. But the force excerted by the second magnet is not strong enough to do so. But one can magnetize a non-magnetic piece of iron (for instance the tip of a screwdriver) by moving it over a magnet.