First and foremost, Happy New Year :-)
The maps on both my sites suddenly stopped loading - the "loading" graphic didn't even appear. I changed themes to three different WordPress default themes but it didn't make any difference.
I then followed the usual troubleshooting technique of deactivating all plug-ins except BGMP (which made the maps load again), and then reactivating them one by one until I found the culprit.
I found it was a new component of JetPack that was introduced with the latest version (2.0.4), namely, Publicize. Deactivating Publicize results in the maps loading again.
I tested further and found that BGMP 1.8 works fine with Publicize activated, which is why I have concluded the problem lies in an interaction between BGMP 1.9.3-rc1 and the Publicize component of JetPack 2.0.4.
Hoping this helps someone.