Can a Sandman Bard use two rounds of his bardic performance to steal a spell with a conductive weapon?
It's supernatural, it requires a touch attack, and he is expending uses of his class ability, so yes.
The problem is, using the touch attack doesn't actually expend any rounds of bardic performance. By RAW, you must start the performance BEFORE making the attack.
Now that I think about it, since he doesn't expend anything with the attack itself, I'd actually say he can do it at will as long as he keeps up the performance.