You are absolutely correct.
I do play a lot every week, but I should get about the same battery life. I don't leave the bass (Stingray 5, not a big battery eater) plugged in when it's not in use. I say a few weeks, that translates to 6-8 weeks.
I've witnessed players in the middle of a tune and the battery dies. I'm uber-paranoid about that happening to me. I've actually handed my bass to a player onstage when his bass quit and (



) he didn't have a spare battery.
9Vs are (relatively) cheap. It's just a choice I made a long time ago with active basses.
Believe it or not, I have on hand one of those John East battery life LEDs. They really do work. I installed them in two basses that I no longer own. I really should install it in this Stingray, but I just haven't gotten around to it for whatever reason.
Line6man, you keep on being correct. I'll keep on being paranoid...
Take care...