Its certainly possible, but its pretty unlikely. Those plugs are well attached to the board and to damage that without other damage would be tricky. You definitely know what action you took to make it happen. Its very rare indeed for card to work and then stop but only on one output port.
I am guessing this is quite an old card and hence replacing rather than RMAing. In which case you might for relatively moderate money get a dramatically faster one, otherwise its worth having a firm confirm (or otherwise) the fault and potentially send you a replacement. That is unless you suspect you physically damaged it, then it would be quite dishonest to do so and should purchase a replacement.