Personally, I think the problem isn't the system, but the assumptions behind the system. A magic user in D&D can't meaningfully contribute to very many battles before using up their good spells. This leads to prioritization, which while potentially cool and tactical, is boring; it leads to battles where the mage is left in the back waiting for the battle to end. This is compounded by auto-attacks for non-casters, which doesn't work well for video games as it leads to the player also sitting around waiting for the battle to end. It's especially problematic when there's little way to avoid taking SOME damage, turning it into a matter of attrition. Because of this, the system has to allow some way to recover, and the D&D solutions don't work because the assumptions between pen and paper and video game RPGs are different.
My suggestion would be to not base it on fatigue or sleep. Instead, tie the magic limitations to backlash. You could have subtle affects that merely bend the laws of reality; these would be less powerful but more readily available, the kind of stuff your mage can do on a small scale to help out in battle while still keeping the 'big guns' for the more dangerous foes. Then you would have overt effects which outright break the laws of reality, doing impossible things - turning someone to stone, a lightning bolt out of a clear blue sky, etc; This stuff would cause a build up of negative forces in the mage which have to be safely vented or else it causes some deleterous effect. Venting would be done through meditation, with each hour eliminating one unit of buildup. Of course, this process couldn't be interrupted without consequence, so while you could do it anywhere, if some hostile force happened upon the caster his companions would have to protect him or risk the process backfiring spectacularly, even worse than the mage pushing themselves with lots of buildup.