I'm afraid the issue must be something on your end.
I've tested using both 2.4Ghz and 5Ghz Wi-Fi and on Firmware 1.00 and the latest 1.20. On each test I transferred 100+ large JPEGs without any issues. I shot in bursts and moved between rooms.
My initial guess would be 'Signal noise', but since you say you experienced it on another wi-fi network too, that's probably not it. Unless both places are very signal-noisy.
In case it's because you're using a firmware version that caused the problem (somewhere between 1.00 and 1.20) then you can get the latest version here:
https://fujifilm-x.com/en-us/support/do ... eras/x-h2/You can check your current firmware version by holding down then "Disp/Back" button on the back of the camera and then turning it on.
I'm not sure where the antenna is located on the camera, but in case you normally grab the camera tightly in specific places and inadvertently block/reduce the signal, you could try not to - while testing - to see if that changes anything. And if it does, try holding it differently.
Your camera could of course be defective, but that's usually not the case.