The fact with IMAP is local settings are mostly ignored as the server is considered canonical for the synchronization. I suggest you look at the policies of your providers. Not that I am aware of either yahoo or GMX having such policies.

It may be a mobile mail app that is making the changes. In a synchronized world determining exactly where a change event comes from can sometime be a challenge. Do you perhaps have two of the accounts configured on another device and not the Gmail one?

Hi Matt: Thanks for replying. I have all 3 of my accounts on multiple devices and it's only on my new computer that the older emails are being deleted. I went through every tab on the Thunderbird Account Settings, and the only difference I could find was that in Synchronization And Storage, in Disk Space, under "To recover disk space, old messages can be permanently deleted, both local copies and originals on the remote server.", all 3 accounts are set to "Don't delete any messages" and "Always keep starred messages" as on, while "Delete all but the most recent messages" was set to 200 messages on the Yahoo and GMX and 2000 on Gmail. Since, in all 3 cases, "Don't delete any messages" is checked, I don't think this should make any difference, but I have changed all of them now to 2000 messages to match Gmail. The only other thing I can think of, which is actually where I think the problem lays, is that I set up Thunderbird to automatically compact folders during installation on my new machine and I didn't do that on my other devices. I'm not sure if this would cause my problem and I'm also not sure how to change that setting. If my problem continues and no other solution can be found, I guess I will try completely uninstalling Thunderbird and then reinstalling it on my my machine with that setting not applied. I'm not sure if that would help or not but I am running out of ideas to try. Thanks a lot for your help.

Gmail by default will delete any emails older than 30 days that are in the Trash or Spam folders. If you select one of those folders and it gets synchronised with server Trash/Spam it will only show what is on server, so may appear to suddenly lose emails. https://support.google.com/mail/answer/7401?hl=en&co=GENIE.Platform%3DDesktop

Emails that lose the 'Inbox' label will still be in the gmail 'All Mail' folder, so you can easily log on to gmail webmail account and reset the label. Worthchecking to see if emails are still on server.

Yahoo also auto remove deleted emails, but they deal with Trash every 7 days and Spam every 30 days. https://help.yahoo.com/kb/trash-spam-folders-regularly-emptied-sln3518.html

gmx default time in Trash is one day, but it would seem you can tweak the settings according to info at link. https://support.gmx.com/email/organizing-and-searching/trash.html

However, if the phone can still see emails then it is likely the phone is using POP in which case if the phone pop account settings do not say to 'Leave message on server' then when phone downloads emails, it will get removed off server by default. Then when the Thunderbird imap account synchronises with server, it can only display what is on server. This would fully explain why emails get removed from an imap account 'Inbox', but not from the phone. You need to see if the emails are still displaying via accessing the webmail account for Yahoo and gmx. If not on server then they are not doing to display in an imap account, but they will display in a pop account.