- Is someone syncing this calendar with an Exchange server or auto-exporting calendar events to a non G-Cal program that wants to move rather than copy the sync'd events?
- Does anyone have an IFTTT (if this then that) rule that processes new calendar events?
- Create one test event per person in this group, share it with just that person, and see which of the 20 events disappears shortly after creation. That'll discover which of these people have the problem-causing software. Then you can ask them what calendar tools they're using.
Addition: From the comment, so you're not adding any guests to these events, just putting them on a shared calendar?
In that case, do a different experiment. Temporarily remove half the people from the shared calendar, add an event, and see if it disappears. The first test will narrow it to 10 out of 20. If the event disappears, focus on that 10. If it doesn't focus on the other 10. The second test will narrow it to 5 out of 10. Then 2 or 3 out of 5, and so on.
Assuming only one account is causing the problem, you'll know which one in 4 or 5 trials.