That’s the question being asked over at The Monkey Cage. I don’t have any hard data, but my anecdotal memory says:
1) In general, not very often.
2) The losses comes in a bunch of flavors: pulling a doomed bill prior to a vote (ex: Boehner debt bill, July 2011), losing a final passage vote (ex. TARP attempt #1, September 2008), and losing a vote on a rule (crime bill, August 1994). The leadership pulls bills that are going to lose more often than they actually lose a vote. My sense is that rules votes fail less often than final passage votes, but they are both rare events.
3) The most recent final passage loss I can remember is TARP attempt #1, September ’08. Three years ago next week.
4) I can’t remember a rule going down during that time period.
5) My intuition is — and again this is anecdotal — that the majority leadership lost more often a generation ago, in part because the parties weren’t as ideologically homogeneous, in part because the leadership had less control over the backbenchers, and in part because the leadership was generally more inclined to let bills (like appropriations bills) come out of committee and onto the floor relatively un-vetted and under open-rules.
If you have insight or hard data, I’m all ears.