It does stabilize...took me about a week. However, what you really wanted to do is to decrease your dosage. When I came off of it, the schedule went from 50 mg (my initial dosage) to 25 mg for one week, then to 12.5 mg for one week.
The safer way would have been cutting the pill in half to 50 for one week, then 25 mg for the next week. I am not a physician, but I believe the 25 mg is the lowest therapeutic dose and the level at which you could safely discontinue it.
The problem is the rebound effect you are experiencing, where your heart rate is elevated for some time now that you don't have a constant dose of a beta blocker to attenuate it. Even when I discontinued it from 12.5 mg, I remember a slight bit of elevated heart rate; although, not up in the triple digit range.
Good luck,
Ulrich