Since OS X Mojave my Apple mail stops getting new emails every few months. This seems to occur with each new OSX upgrade. (e.g. 10.14.3 to 10.14.4) The mail app loses the password for the Gmail accounts, a lightning symbol appears next to each account, and no new emails come in.
There’s a simple fix, but it’s not obvious.
You need to click on the lightning symbol and re-enter the password for each Google Gmail account. In my case I needed to get each family member to click on the lightning arrow and re-enter their email account password.