After using my rainbow key, took 2 waves of enemies down and then no more appeared for the remaining time. Thought it was a fluke. Went and used one of my Tokyo gold keys and after 2 waves, it did the same thing...nothing showed up, but I remained in the area...

it happened to me aswell on tokyo rainbow key, just only two waves it just somehow didnt spawn anymore enemies while theres still time.

This usually happens due to connection issues or a desync. Desyncs will still allow you to stay connected, but the server is having trouble with talking back to your client.

There's no way you'll be getting your tickets back by the way. When you accept the mission at the yellow/gold barrier, you have to pass through a confirmation dialogue box stating that you agree to use the ticket item, and it will be consumed.