They indeed never tried, but had they the likliness of success seems to have been slim:
1) Although Hitler forbid the 6th army to simultaneosly break out, Mannsteins troops mounted a serious attempt to break the Soviet encirclement. Although his troops were in much better shape, relatively fresh, and well supplied in comparison with the battleworn 6th army, they hardly got halfway, so even with an all out attempt at breaktrough by the 6th army it seems unlikely that more than a few small units would have gotten through.
2) Even when mistaken by such assumption, would it have been wise to break out in November '42? Almost certainly not as the 6th army would have had to leave all heavy material behind and no defensive positions in the hinterland whatsoever had been prepared. Such a breakthrough/retreat might easily have turned into a rout if the Russians had choosen to go in pursuit, (for which they certainly had the means), thus doing more harm to the Southeastern front as already was the case.
3) More important: German panzer troops were still in the Caucasus and a hasty retreat of the 6th army and relieving troops after a successful breakout would have badly jeopardized their position, in all likeliness resulting in them being cut of. 6th army remained at Stalingrad and thus made possible an orderly retreat from the Caucasus.
4) Concluding; Although by no means wanting to bestow on Hitler the title of great stategist, his order to stay put at Stalingrad seems right as anything else would have led to greater damage.