Generator won't power my AC unit

[Fedfire37]

I have a 93 Gulfstream Innsbruck that I fixed up for a hunting camp. It has a Coleman Mach 13,500 BTU roof unit which I assume is original equipment. This week I tried running it on low with my 3500 Watt inverter generator. It kept shutting the generator down.
I also have a 2015 model Crossroads travel trailer which has a Coleman Mach 3 AC 13,500 BTU unit. I used it all last summer with the AC on high on generator power with no problems. If I ran the AC on low the generator would even run in eco mode at lower RPMs.
What could be the big difference here? The Gulfstream's AC ran fine on shore power when I checked it.

[atreis]

There's a capacitor (soft-start capacitor) that helps the unit to start up without drawing a huge amount of power. Those go bad ... Once it's running there's usually no issue keeping it running. It's that startup load that causes problems. No idea how to find and replace it but some searching on Google and YouTube would likely point the way.