Is this a new problem, or was there a time when the robot didn't continuously reset? If a new problem, are you aware of any environmental changes that might have contributed? Have you tested the supply voltages--voltages that are too low can cause "brown out" resets in some processors. Have you looked for spikes on the power lines? And, if there is a reset circuit, perhaps the problem is there.
If this is not a new problem, then perhaps there's a watchdog timer running,that you aren't aware of. Is this something you built/programmed yourself?
And, if you programmed this yourself, and used something like C, then perhaps there's a pointer running off the end of allocated memory. Or, is there anyplace where you are calling a reset in the code -- perhaps the logic is incorrect.
Is the controller directing driving anything? Perhaps you're exceeding the power spec. The controller might reset if it's getting too hot, etc.
Assuming some kind of arc welder (or other type of welder that uses electrical power) is the controller on the same supply line as the welder? If so, the welder might be causing the supply voltage to dip (thus causing a reset in the controller).
And, as Nihkil inferred, we will probably need a great deal more information to even begin to help diagnose this problem (unless, of course, Colin got lucky ;)
Like, details on the electronics (schematics, etc.), a listing of the code, a description of the environment the robot is in. My knowledge is limited to a subset of the PIC uController line, so, if it's anything other than that, I will be of limited use, but maybe someone else will be able to help.