Why does it say your connection to the show online has been lost?

Most likely its typical launch day issues.

You would have to contact Sony support for their game.

https://theshow.sonysandiegostudio.games/hc/en-us

Surely it cant be that hard to tell if they lose connection? It even gives you a bleeding message saying "Connection to your opponent has been lost". So surely it can easily determine who quit and who lost connection?

@Y2JEH nope no errors or nothing just says ''Your connection to Xbox LIVE has been lost. Please sign in again.''

When you get disconnected from the game, does it say, "your connection to xbox live has been lost"? If it does, that is an issue with your profile in addition to your NAT issue, for that you just have to download your profile. To do that you press
the guide button, if you're signed into a profile, press X to sign out. The select download profile.

Don't panic, got 1 game played then hit with "the connection to ea online has been lost" wonderful