It sounds like everytime your IP address changes, you have to login with your webbrowser, even when using IMAP with SSL/TLS ("less secure") enabled on the GMail account.
I have a couple of GMail accounts myself that use the "less secure" setting and I've never had this problem; but I leave my modem on 24/7. I'll try releasing the IP address and see what happens.
...
Ok, I confirmed I got a different IP address, had PP log back into the accounts and no problem.
hmmm... is this new in GMail's standard FAQ (
https://support.google.com/mail/answer/78754)
"Make sure your mail app isn't set to check for new email too often. If your mail app checks for new messages more than once every 10 minutes, the app’s access to your account could be blocked."
I don't recall having seen that before. With that consideration, make sure that you have IDLE enabled (edit the account, it's near the bottom-right) as this would significantly reduce the number of logins required. Even if you have a 10-minute polling interval, there may be other reasons why PP would need to re-login, such as to retrieve or delete messages (that still shouldn't be a problem with *default* settings in PP).
Also, as is mentioned in the other thread I linked to, you may try enabling 2-step verification and see if that helps. Even if it does -- if you don't want to use 2-step -- try disabling 2-step again (re-verify that "less secure" is enabled) and see if it works better.
