Magnets don't run out, though it is possible to ruin them by banging or heating, etc.
If the magnet is strong enough to pull the ball up the ramp, then it has already lifted it against gravity to where the hole is. Of course it is pulling up the ramp, so the force of gravity is reduced (draw the force diagrams!).
Now the ball reaches the hole; if the magnet is really strong the ball is going so fast that it hops across with a slight bump. But suppose the magnet is weak enough (or the ball heavy enough) that it will fall down the hole (draw the force diagrams required for this to be true!).
Now when the ball reaches the bottom of the hole it is supposed to fall down a second ramp which should lead it to the first one (I'm imagining something like Mousetrap, the game - but you must draw this in some detail).
I am here interested in this second ramp: it clearly has a slope that is gentler than the up-bound ramp, because it starts at the bottom of the hole.
Now draw the force diagram for the ball at the top of this second ramp. Since the downward force for gravity is the same everywhere, the effective lift required to move against it can be determined from the slope of the ramp.
You can also say something about the force from the magnet: it has to be large enough at the bottom of the first ramp to get the ball rolling, and then increases (1/r^2, approximately, from Coulomb's law for magnets). You also know that the magnetic force at the top of the hole is insufficient to keep the ball going, and is not sufficient to keep it from falling down the hole (by assumption!) ... so once again you have a limit on the force vector from the magnet, in this case in the vertical component at the top of the hole.
Having analyzed all of the parts, and established the limits of the magnetic force at various points along the way, for your final step you must draw the force diagram for the ball rolling down the lower ramp. Since at the end it must come out level with the up-bound ramp, or be higher up, but with less slope, it seems to me that the magnet will impede the downward rolling motion of the ball ... and it will freeze up on the way down.
You should be able to show this with the force diagrams, no matter what the design of the contraption is.
You can also construct a working model, and let your friend try different sized ball bearings, and reposition a very strong magnet as required to get the ball moving.
Note that we don't rely on friction or failing magnets here.