The zombies take critical hits like getting their limbs chopped off yet as soon as they regenerate they show no signs of fatigue or slowing down. Now their chakra whilst being spiritual energy has to have some sort of relationship with their physical being, it can't exist as an abstract. So if you for arguments sake completely destroyed an Edo Tensei zombie there would be nothing left of him until he regenerates. If his chakra is seperate and detached from the physical body then where is it now stored whilst the body comes back together again?

It can't be dependent on the hosts chakra either, as the people being summoned back are some of the biggest bad asses in history and thus capable of using jutsu that use huge amounts of chakra (like Kinkakku and Ginkakku). They would have used up the hosts chakra in an instant if that was the source, especially with their special weapons. It can't be Kabuto's chakra either, as then the Edo Tensei would be like a Kage Bunshin type jutsu where the user splits his chakra up amongst his clones. As we have seen only Naruto is able to make mass clones due to his huge chakra reserves. Even then he is making copies of himself, not Kage level ninja's with magical weapons etc.

The only place the chakra could be coming from is the zombies themselves and like their physical bodies it must be constantly regenerating. As for the perpetual motion machine problem - this is Naruto, normal physics stopped applying a long time ago.