I'd say no, they should not. When I find ANY weapon, I want to keep it until I decide I don't want it anymore, I don't want to lose it any sooner, unless I must give it up to complete a quest (I mean things like Umbra in Oblivion where you had to choose to give it to Clavicus Vile and get the original promised reward or keep the sword.) Losing them due to running out of charges (Weapon charges should be removed from the game anyway I'd say, or at the very least, return to recharging over time like in Morrowind.) or broken, and especially due to time since you have no way to stop that from happening would just be EXTREMELY annoying, the fact that artifacts have been known to migrate between users serves to explain how they can appear across multiple games even though each game may be set far away from the last time, but it should remain as that, I don't need it to be reflected during the game.
Besides, Bethesda needs to focus on making sure each Daedric quest is interesting, not letting us repeat them, I don't want to repeat a boring quest.
Well I also said I'd only want it if you can get 'em back... and (I didn't say this but) they'd have to be much more powerfull, and have larger charges.
I'd rather weapon charges go away entirely, I don't take any pleasure out of having my sword have limited ammunition and needing to reload it every so often, I want to deal with ammunition, I'll stick to ranged weapons.