Examine your shore power cord closely for signs of heating which would indicate a poor connection or broken wire inside the cord. Pay particular attention to the plug itself looking for loose prongs or sign of heat.
Follow the cord to where it ends inside your MH. Look to see if you have an EMS system installed (Progressive Industries, SurgeGuard, etc). That might be sensing a voltage problem, or might be defective and false triggering. If you don't have an EMS, then the shore cord should connect to your ATS. There could possibly be a failing contactor or control board in the ATS. There could also possibly be a loose connection inside the EMS (if you have one) or ATS where the power cables connect. Make sure you disconnect from all power before you check those connections.
How frequently does it do this? Can you have someone listen to the ATS to hear if the contactor drops out when the power fails?