I've had this (although I wasn't playing at the time) after drinking a lot of alchohol, so it sounds like the dehydration problem could be spot on, and I'd echo the statements at looking at your technique.
Neon Avenue
Not the wierdest name ever, but the wierd part was all the rumours partially invented by some of the other members that it was the name of a street in America somewhere dedicated to gay bars...apparently
I own a Custom-5 and after I restrung and gave it a setup the B-String was fine
As for Batteries, I used mine for atleast 5 hours a week, and the cheap battery that was in it lasted 5 or 6 months since I bought it
See if there are any Open mic nights/Jam sessions in your area and go to them, good way to keep your playing standard up/improve regardless of if your in a band or not :)