I've been having a strange issue with future calendar entries disappearing for a while. I'm finally able to reproduce the problem. I have an iPad mini running iOS 9.3.5 (newest version it supports).
When I click on a link such as this one and select download to calendar it prompts me to add it to my calendar. After adding it, the entry appears on my calendar as expected.
If I then go into calendar, tap on the event, edit, change the reminder alert time, and tap done, the entry disappears from the calendar. I can reproduce this every time. One clue I noticed is that if I turn off iCloud for the calendar before I add the entry the problem does not occur.
It only happens when creating the invite via a link. Events added manually never have this problem. I've tried toggling iCloud on/off. That didn't bring it back. I also verified that I am not over my iCloud disk quota. Any idea what is going on?