This happened to me just the other day. The FAF of a VOR approach is
the station, so the needle goes full deflection as you reach FAF. You
then have to wait until about 1/3 of the way to MAP before it comes
back in. As long as you were stabilized before loosing the needle,
you just have to stick it out. Of course, one problem is that, with
strong winds, you begin your dive at the FAF, winds shift, and you may
very well come out quite a bit off the center.