Hello,
1) I would try to make sure this is not a physical layer issue. The local loop certainly has changed, so I would consider this factor as the first suspect. If the physical layer is unstable, BGP will flap as a consequence of that (you need proper circuit to run BGP over it). Check this together with your circuit provider.
2) I would check the configuration on both sides. Have you made any changes to any of the routers at either side of the session (or perhaps replaced an entire router)? How often are the flaps? If they are only a couple every day, then BGP configuration is probably ok (if it were not, you would more likely not have a session at all). Check this together with your BGP peer.
3) If everything above is tested ok, you might have a bug or some other strange issue (make sure you have adequate resources for your setup, check if you are under any kind of attack or something).
Kind Regards,
M.