PhotoEngineer has posted on numerous occasions that Phenidone is unstable at high pH. This indicates to me that the destruction of Phenidone goes faster as pH is raised. Now if you look at the average fine grain B&W developer, you have pH of 8.2-9. If you look at E6 FD from the formula I linked to, you see pH 9.6. Therefore I would guess that E6 FD mixed with Phenidone is less stable than fine grain B&W developer mixed with Phenidone.
I wouldn't worry about it going bad in a day or two, but I wouldn't use it over a much longer time span. Mix the chemistry (1l per 10-12 rolls of film) for as many rolls as you can process within one or two days, use it, then discard. Not much different from using a regular kit, just a bit less time to process a batch of films.