I finally found someone else having an issue with a similar Modem: http://forum.mikrotik.com/t/lte-interface-drops-consistently/113684/1
My modem is a Novatel USB730L, whereas in that post, it is a Novatel750.
The fact that I have fewer issues with the full USB router makes me think this is more of a localized issue than firmware, but is Mikrotik still working on getting these modems working? I believe they only became supported in 6.41.