GFI Outlet Tripping (A/C and Extension Cord)
AC units and GFCI’s don’t always plat well together. I would bet you could plug this directly ac directly into the GFCI and about the same cycle would occur.
This happens all the time with Refrigerators and freezers , just search the site for proof. The GFCI receptacle should be unaffected by a 50’ extension cord of that large gauge. not much difference than using the load terminals on a GFCI circuit.
The manufacturer says not to use extension cords to limit their liability but 1200w would work fine on a 14 awg cord.
Why is the GFCI tripping out after a few seconds?
The electronics first turn on then the fans then the compressor itself.
The compressor is likely causing enough of a phase shift at startup to trip the GFCI.
The reason is motors are inductive devices and when they first start their ac resistance is near zero as the high current incoming is almost pure inductive there is a 90 degree phase shift in voltage and current. Most use a capacitor to cancel the shift and provide true power for starting. This phase shift is seen on inductive devices and most likely the cause for the tripping.
You can prove it’s the AC and not the cord by plugging directly in to the outlet.
There are many such questions on this site.
The phantom voltages mentioned by others has voltage but no current it takes current at 5ma to trip a GFCI. The instantaneous load of a 1200w system will be close 4000w and the large phase shift due to inductance causes problems.