We've been having trouble sending iMessages with photos for the past couple of months. We are using iPhone 7s registered with different carriers, both running latest iOS. Text-only iMessages have been sending just fine, but those that have photos will time out. I read through a thread about an iMessage outage early last year that recommended that we change our DNS settings to Google's servers (22.214.171.124) but that doesn't resolve the issue. I've also rebooted the modem and the router and made sure that both have up-to-date firmware. Is anyone else having this problem?
I don't have any iPhones so only guess but possibly something on Apple's side has changed that doesn't like the latency and/or satellite in general. Known issue already that cell calls over WiFi pretty much doesn't work with satellite Internet.
Also could be the large file size with photos. What size are you sending? HughesNet upload speed isn't the greatest in even the best of circumstances.
Have you checked the Apple forums?