My experience is that the time it takes for the batteries to go dead after the warning tone varies greatly. I have been using Power One batteries exclusively since I got my HA’s, which are Phonak NIOS.
So I have no experience with other brands, but the Power One cells vary from dying almost instantly after the tone, to lasting a couple of hours, with the tone going off every 30 min or so. Rarely do they last more than that. Obviously, if your aid is working hard when the tone sounds, then you’ll have less time before the battery dies completely.
I always carry a spare pair of cells in my pocket, protected by a battery caddie so my keys don’t short the cells out or rip the tabs off.