Network Error...in every gym battle I do. What can I do???

There is nothing you can do.
I find that restarting the app before trying to take on a gym can sometimes mean you can go a little longer before it happens...but I am yet to find a way to stop it altogether (apart from using a different device)

As soon as you notice the battle is "hanging", turn off/on your network and hope for the best. With luck you have lost only 30s. It's sure annoying to find out that battle hanged at 80s and it resets fight with defender full hp, I took serious beating and 40s time left.
Tip. Avoid gym battles. It will drive you mad. If you have to prestige, do it with higher cp pokemons so they can take some beating, while preventing time outs.

if your wifi turned on?
When I'm out and about I turn it off- way less issues.

I know, right?

I error out about every 3 minute of gym time. Sometimes just scrolling to pick my attackers. The only thing I hate more in the entire game is spoofers