It depends on the quality of the current parts. If the wheel has a decent hub and rim, new cones and nuts are a dirt cheap way to keep it running. $50 pre-built wheels are pretty much the lowest quality out there, so unless the current wheel is garbage, I'd keep it.

As for the bike itself, if the frame or fork is damaged or compromised, that would certainly warrant a new one. But if it's functioning to your satisfaction, I'd approach it on a part-by-part basis. You'd have to significantly upgrade a lot of components before it would be cheaper to buy a new bike.