IIRC Sandy King said in his first articles on Pyrocat that the mixed developer lasts only an hour or two.
Yes, that sounds about right. It's certainly still active after 45-60 minutes, at least without too much agitation. Beyond that point, it'll start to taper off.
Do folks tend to simply mix what developer they will need for an evening of processing films and store away the rest of the concentrate?
That's the way it works for many developers, yes, although not all. For instance, developers like XTOL and D76 are packaged with the intent that you mix it all up, and then either use full strength, or dilute only a little further before use, and possibly being reused and/or replenished. On the other hand, developers like Rodinal, Pyrocat and to a lesser extent also HC110 are designed to be diluted down quite far to working strength immediately before use, and then discarded.
In general, if you need to dilute a lot (ratios of 1+25 and higher), it's safe to assume you have to dilute immediately before use and discard after use. With developers you mix from powder or that are used at low dilutions (less than 1+10), there's a good chance that they'll keep in liquid form fairly well and might be reused.
Pyrocat with its typical dilutions of 1+50 ~1+100 clearly falls in the former category. Since it essentially lacks antioxidants, nothing protects it from oxidizing under the influence of the oxygen dissolved in the water and thus, it has a very short life once diluted to working strength. Developers like D76 and XTOL on the other hand are positively loaded with antioxidants (mostly sulfite) and thus, they tend to survive much longer. Paper developers also generally fall in this category, which is necessary because they're used in trays (large surfaces that will promote oxidization) with frequent agitation and for hours on end.