What kind of failure was it?
Did the flaps fail to fully extend?
Was there an asymmetry?
Did they retract uncommanded?
At first glance, I would have re briefed (@3nm) on the approach for a partial flap landing, selected a new Vref, and landed with extra autobrake. Perhaps the type I fly B757/B767 lends itself to be able to do this more. At 3nm on a B757/B767 you would at least be @ Flap 20. Landing with Flap 20 or 30 in a B757/B767 makes little difference to landing distances. But again perhaps this type is not "normal."
If the flaps had retracted uncommanded, or had suddenly developed an asymmetry then I wouldn't be convinced they would retract for the go around (assuming single engine, as you have to do.). At that stage in the approach I think it would be safer to land. If however you type is prone to such problems, and they are known then a go-around is probably the best answer. I think the answer to your question is, it depends on the type!