Hi, I'd be more inclined to think the color developer would go bad first, because color developers use relatively small amounts of "preservative". But I don't know my way around E-6, only the color neg/paper processes.
Still, I'm sure you COULD reconstitute the bad developer, the only problem is in knowing what to add. Most of the time it's probably not worth the effort. I've done this sort of thing in the photofinishing industry, where it's been cost-effective. But for a hobbyist, I'm very skeptical that it would have any real savings.
If you want to get more life out of your solutions, it would probably be better to use an actual replenisher solution, periodically adding some of this to your used solution. The replenisher is formulated to make up for the specific chemical components that do get used up, at least in a normal processing cycle. For "old" chemicals, replenisher is not ideal, but it should "sort of" work. Best would be a special type of replenisher intended for "low processor utilization."
BTW, the normal industry terminology for these things is: the solution in the tank used for processing is called "tank solution" (what most photogs call developer, etc.). The solution you add periodically during processing, as a "boost," is called "replenisher" (the replenisher is designed to maintain all the chemical components in the processing tank at the spec concentration). And finally, for the surplus solution (as a result of adding replenisher) that can be reconstituted and reused, sometimes "regenerator" mixes are available; these essentially convert that used chemical back to replenisher. (Other treatments, such as silver recovery, are generally necessary before regenerating a processing solution).