Mojave Mail.app issue - Gmail accounts *constantly* disconnect themselves! All was fine up until a few weeks ago.

I have two none-Gmail accounts that always stay connected no matter what. Lately, the Gmail accounts have constantly been disconnecting.

All the accounts with connectivity problems are Gmail. If I click the little 'disconnected' icons it connects ok and retrieves any mail. They will then stay connected for a while before all eventually disconnecting again.

All the accounts with red dot are Gmail. Despite what it says, there's no need to verify if the username and password are correct – they are. Nothing has changed. As I said above, I can manually connect by clicking the 'disconnected' icon. They will then stay connected for a while before all eventually disconnecting again.

Before I take the drastic step of nuking my Mail.app settings, preferences, Library/Mail folder, then re-adding all the accounts from scratch, I'm curious if anyone else is experiencing this or has a solution?