Love your database. Keep expired events under control.
Visit Events > Settings > Housekeeping ... if you can't see this tab then make sure you have activated the plugin, first of all! Remember also that the current version of Housekeeper is built to work with The Events Calendar 3.0. If for example you are using a much older version then it may not work.
Assuming the expiry criteria is being met then this could be a problem where local loopbacks are not allowed within your hosting environment. Housekeeper relies on something called "Scheduled Tasks" so that it can work its magic in the background, as it were. However not all hosting environments are conducive to this. If you think that might be the problem then check in with your hosting provider and/or search for "alternative cron solutions".
Any instances of recurring events meeting the Expiry Criteria are deleted - those instances not meeting the criteria are preserved. This seemed like the most logical way to approach recurring events but any other ideas are welcome.
That's completely possible for a variety of reasons. First of all, ensure your server and WordPress date/time settings are correct. Second, but more importantly, back-up before you use it and then keep on backing-up, frequently and often. You should be doing this anyway - and remember! - a back-up is useless unless you know how to restore it.
They are deleted out right. So don't confuse this with the "Trash" function WordPress provides for pages, posts and many custom post types. With this plugin, any events deemed to have expired will effectively be wiped out forever.
In the eyes of this plugin an event has expired after it has started and this is flagged up in the settings tab. That may not always be ideal - and for those cases you can adjust the expiry criteria appropriately or just deactivate this plugin.
Please post details on the forum. Better yet, post a fix and add appropriate details. This is free and open source software and comes with no guarantees, so bear that in mind first of all.
Feel free to post on the support forum, but remember that support is not guaranteed (nor is the plugin) ... after all, it's free.