Note that Mike is talking about mixed chemicals. I don't know how much chemical volume you need in your Phototherm, so that'll be an issue. If the Phototherm takes reasonably small quantities (say, 250-500ml), then you won't be very bothered by the short keeping time of mixed chemicals, even with the 1-2 rolls/week you mention. If you need to fill the Phototherm with, say 2000ml of each solution, then the relatively short keeping time of mixed developer will become an issue.
Unmixed, E-6 can last for months, particularly if you transfer the more sensitive concentrates to full-to-the-brim glass bottles. I've got a Kodak E-6 kit that's over a year old (probably over two years), and until recently it seemed fine. My last E-6 roll didn't fix properly, but the fixer isn't showing the obvious visual or olfactory signs of having gone bad, so I suspect "pilot error" on that. (I re-fixed the roll in C-41 fixer and it's fine now..) Note that this kit is a Kodak 6-bath kit. The E-6 kit I used before was a Paterson 3-bath kit, and it went bad much quicker. The 6-bath process is much more of a pain to mix and use, but I trust it more than the 3-bath process used by some of the third-party chemical vendors.