Could be wires as indicated. I'm only familiar with the single cylinder kohler models. Does the twin onan have two coils? If so it could be the coil or condenser (if yours has one) on the failing side. Coils and condensers sometimes only begin acting up once they warm up or are put in higher throttle as they near full failure.
Also...can you elaborate on the air gap? Was the needle not seated properly or did you mean the carb was not mounted tight enough against the motor and was drawing air in that way?
Most Onan's have one coil that fires every revolution so it catches both sides. If it's not firing on one side, I would look at that plug/wire.