Of course, that depends on the battery. Here are some observed runtimes in hours and minutes. These values apply only to the WRT54GL which is the most energy efficient variant of the WRT54G. Generally, the older the model of WRT54G you have, the more power it will use and the shorter the runtime will be.

The input voltage range requirement spans at least from 16V down to 4V. The one-time use batteries were run down to below 3.5V, where the router stops operating. The rechargeable 12V batteries were run down to 11V where you can expect a reasonable number of recharge cycles. In an emergency you can run the SLA batteries down to 3.5V and the runtime will be extended at the expense of killing the battery.

And as a reference point, it was found that a 55 AH SLA battery with a 45W amorphous solar panel under decidedly sub-optimal conditions can run a WRT54G indefinitely.