One issue is that is the biceps tendon comes out with too much force (e.g. something slips during a deadlift) it can tear your labrum. This is because it passes through a sheaf connected to the labrum. It can also blow out your subscapularis (biggest and strongest rotator cuff muscles). The latter happened to me -- partial tear with tendon rupture some years back the full subscap tear. Just had it re-attached.
It is a waste of money to have the PT put it back in, unless they really know of a way to make it stay. By all means try conservative options but look into either a biceps tedonesis (re-attach it elsewhere) or a tenotomy (just cut it). Remember that the long head of the biceps works as a shoulder stabilizer too, so you might actually be seeing a symptom of a shoulder dysfunction. That's the first place I would look for a conservative approach. If you can figure out why it is getting so stressed, maybe you can modify your training to avoid it. Surgical options are a last resort, but read up on them so you can get a good idea what it means for this to take a turn for the worse. Better to know that now and keep an eye on it.