Minato stated that hirashin and the vines have drained his chakra which means that EDO chakra reduces upon using their techs.
Also Itachi's response to Sasuke's question is an implication that his chakra can run very low and be unable to use his Susano at some point. Sasuke doesnt know much about EDOs but he has sharingan and can know if Itachi's chakra started getting low.
EDO having unlimited chakra doesnt mean they have infinte pool of chakra at any instant which contradicts Minato running out of his chakra. It means that their chakra can regenerate at some rate but definitely not instantly , or minato should have been able to use hirashain and Save Naruto, and, unlike living shinobies, running out of chakra wont cause them to die so they will be still able to regenerate their chakra and continue.