OK - ran it down pretty fast today (fast enough that it has me a bit concerned!):
When it got low, there
was a voice alert warning about the battery. It repeated again, but not for several minutes.
So I guess it is working, and I must have missed it the other times. I guess I was expecting the frequent, repeated tones that all my other phones used - loud and often enough in fact to be annoying, but definitely gets the point across. I kind of wish the TP2 did that, or at least gave me some other options for the alerts.
Thanks to all for the help here, and sorry about the false alarm...