One thing to know is that an AC unit draws 50-60 amps inrush current on momentary startup, compared to around 12-15 amps running current. Inrush current can cause generators to struggle or stall which is why larger generators and/or hard-start capacitors can overcome this. Your gen. size should be adequate.
A hard-start capacitor or Micro-Air Easy-start unit reduces inrush current, enabling AC units to start up. A hard-start capacitor which are around $30 or less compared to $300+ for an Easy-Start unit. Could be that your existing capacitor may need replacement or sometimes weren't supplied by the manufacturer. Good article
here.
