Rest does not always mean sleeping though.
I know there's been several times in the series where a character claimed to be "completely out of chakra", yet the fight continued for awhile, and then, later on, the character would use another jutsu anyway. Which gives the impression that chakra will recover on it's own if you just stop using it for awhile.
Basically what it comes down to is, while I agree zombies probably have unlimited physical energy, chakra also requires spiritual energy as well. So until the give some indication that that is also constantly regenerating, I'm not willing to assume the zombies have unlimited chakra.
Summon another zombie first, remove it's free will, teach them Edo Tensei, and give them very specific commands to bring you back and leave you with your own free will, then dismiss the original zombie so it can't be used to undo the technique.