I assume this is on alto playing classical music. If it were on tenor playing jazz, I would say you are biting too much. Otherwise, loosen up a little and engage in a little kissing therapy;-)
Seriously, my bottom teeth are a little uneven, so when I played lots of classical alto (must have been in school), I would cut a small piece of denture pad and cover my lower teeth to protect my lower lip. Worked great. Part of the problem may be your emboucher muscles are getting tired, so you start to bite more to keep things going. In time, your lip should get tougher and emboucher should strengthen, which is better than a lip protector.