Just had the exact same problem about 2 months ago. Went to exercise the Onan 7.5 QD one weekend and had no 120 volt power from the genny into the coach. The Onan generator was doing exactly what yours is doing which was odd, it never idled that low before. Turned off the genny, plugged back into shore power and had 120 volt power into the coach. Unplugged the coach, fired up the genny and pulled off the electrical access panel on the right front of the genny. Had 120 volts there so that pretty much ruled out the genny, thank goodness. That can get real spendy in a hurry. Was pretty sure it was the ATS.
Had my mobile RV mechanic come in and make the final diagnosis and do the repair. It was the old Todd Engineering PS-250 transfer switch finally giving up. He replaced the Todd switch with a Progressive Dynamics ATS. Was an exact replacement which is a big plus unless you like re-routing huge cables and using bad words. 2 hours labor and $180 bucks for the transfer box and all was well.
2000 HR Imperial 38 WDS
350 Cummins, Aero Muffler & AFE Filter
980 watt solar, 600 amp/hr LiFePo4, Victron