Do magnets have infinite potential energy? Pardon me if my question sounds "out there", I've been out of touch with recent developments in physics, but this is something I've never really put deep thought into.
I know that when two pieces of magnets are bought with their like sides towards one another, they repel, with a force proportional to their intrinsic properties. So in principle you can make a contraption where two pieces of magnets act as a source of tensile strength, just like the electromagnetic forces that exist within metal wires that help them keep their shape under some tension.
My question is regarding the extent to this supply. Can these electromagnetic forces forever hold out the tensile forces against which they've been put to or do they decay over time (let's ignore environmental effects)? In other words, if I have a weight suspended on the top side of a two repelling magnet system, will that weight stay there forever? I can also ask it in another way:
If we have a piece of metal, we know that it has a large number of free electrons that help it maintain hardness. How long will it stay hard for? Do we have an estimate if there's a tendency for metals to lose hardness over time due to wearing of electrostatic repulsion between them?
Another way to ask the question would be if I replace magnets with superconducting magnets, which we know should in principle provide a source of magnetic force forever, is there a reason to believe that that will decay in time too?
 A: 
My question is regarding the extent to this supply. Can these
electromagnetic forces forever hold out the tensile forces against
which they've been put to or do they decay over time (let's ignore
environmental effects)?

They will decay over time.
The magnets were created by causing the atoms of the iron to line up when placed in a strong magnetic field. But over time, at any temperature above absolute zero, the atoms will move around and randomize their positions causing the magnet to slowly weaken over time. Of course, the process can be sped up by heating or dropping the magnet.
Hope this helps.
A: No.
First, potential energy can not be infinite - by definition.
Second, nothing is infinite. Everything will decay over time.
If you put something on top of a table and nothing happens around, then the "thing" will stay there as long as its lifetime ends - but that does not mean that the object has infinite energy.
A: Simply "holding something up" does not consume energy, therefore being able to hold something up forever does not mean an infinite supply of potential energy.
Consider a table in an everyday setting (i.e. near-Earth gravitational field). When you put a weight on the table, it stays there. The table supports the weight, while Earth pulls on the weight with gravity. The weight do not move because the net force on the weight is zero. Therefore, the table does not do work on the weight, thus the table does not transfer any energy to the weight. The table does not need "infinite potential energy" in order to hold the weight up.
The same applies to your question:

if I have a weight suspended on the top side of a two repelling magnet system, will that weight stay there forever?

Assuming the arrangement is stable and the magnets do not decay (other answers have already discussed ways in which magnets could decay), then yes, the magnets can support the weight forever. This does not mean that the magnets somehow have infinite potential energy in them.
A: Potential energy does not changeif you are just holding a body in a field(here magnetic) without changing the position of the body. So no, even if the magnet didn't lose its property over time, it would still not lead to an increase in PE if you didn't push the magnets around(i.e., changed their positions wrt to each other). So no, no infinite PE.
And as Bob D said, the aligned atoms will lose their alignment with time(as they are always vibrating above absolute zero) and the magnetic properties will slowly decrease over time as more unaligned atoms means more of the "atomic magnets'" effects cancel out.
A: Noting is infinite. This would violate the law of conservation of energy. Also, the magnet would decay and demagnetize over time.
