How many postdocs should one usually do before it is realistically possible to get a faculty position?
If you mean a tenure track position at an R1 school, the simple answer is "one" (no more, no less).  And often you will have had preliminary interest (e.g. invited for talks) with some R1 target schools even before the start of the one post doc.  IOW, people already know you are "in the mix" for plum positions.  And you know it, too.

Of course, if you can get such a position with zero postdocs, go you.  But this is still rare, even for superstars.  

If you are heading to your second postdoc, the bloom is "realistically" off your rose.  Look for teaching school positions at best.  Or move to industry or government.  You have too much to offer to wander around doing postdocs for your life.  Academia is a "tournament" job system (Google it) and you are one of the vast numbers of "many are called but few are chosen".

[Note for pedants, the word "realistic" in the question title...]