I admit I’m always a little bit surprised that any limited run manages to recoup, because it’s so expensive to put up any Broadway show in general. But it does happen, otherwise no one would do limited runs with a commercial model.
Like Joevitus said, it really depends on the show. Part of the reason we see plays get limited runs more than musicals is that, in general, small-cast plays are cheaper to put up (because the sets and costumes are usually smaller and simpler) and the overall cost of labor is much lower – because the cast will be smaller, the crew will be smaller, and the creative team will be smaller too (no choreographers, orchestrators, copyists, music directors, fewer writers, etc.) and for that matter you also don’t have to pay an orchestra, which is a huge expense for big musicals. Not to mention, plays will usually be in smaller houses, which have lower rents.
So all this is to say that if you have a lower capitalization, and lower running costs, it’s much easier to recoup on a limited run. Especially when you have bankable stars.
Putting up a musical with a limited run is a really bold move, and I’m surprised any producers even attempt it. But even that works out for some. The “Sunday” revival with Gyllenhaal recouped, and I’m sure there are many other examples throughout Broadway history.