You should get a MicroAir Easy Start. It makes a huge difference. I'm with Zwy, I think it's the batteries falling over with the surge. A normal 4T A/C can pull as much as 28000 watts during startup, meaning your battery has to produce 500+ amps for a moment... If your battery voltage drops too low it's going to cause resets.
I'm running a pair of 18KPV's with 60KWH of batteries. It always started my 4T, when I only had 30KW of battery (600A) but it seriously caused light flickering, UPS clicking, etc. It actually flicks the lights slightly when on grid if you are paying attention.
With the "Magic Start" the UPS's stopped clicking, and I don't really notice most of the time even in the hottest part of the summer on battery. It will likely let you get away with not buying more battery. In the summer peak my 4T can pull just under 5KW continuous (4.87). In milder cimates you will probably get away with something less.