How long a robot will operate on a fully charged battery depends on several factors, and we're by no means experts at this.
First of all, you need to know the capacity of the battery in Amp Hours (or milliAmp Hours). You also need to know how much current the components on your robot pulls. For example, a Stinger Robot Kit, retrofitted with a Serializer, and some Infrared Sensors might pull around 1 Amp to operate.
Once you know how much current your robot requires, and the capacity of your batteries, you can calculate *theoretical* run times. This of course is always more that the actual run times. I'm sure it also differs based on battery technologies.
Here are some quick links for battery run-time calculations I found searching google on this topic.
To give you a rough idea of run-times for our robots, we've had a Stinger + Serializer + IR Sensor last a little over an hour and half, following a line around a course using a 2200mAh 9.6V NiMH battery.