The TL;DR on Apple's macOS Mojave 10.14.4 Gmail/G-Suite Issue: It's Fixed
Same—issue still occurs for me. I haven't had any success by clicking the offline symbol for all accounts, but if I click them individually, it forces them online one-by-one. However, I have to do this constantly throughout the day.
This is a very different problem than the can't-authenticate-at-all issue that was solved a few weeks ago.
I, too, see my accounts offline from time to time, and those times are far more frequent since the 10.14.4 upgrade. But a click or relaunch of Mail fixes it in all cases. Not ideal, but mostly just an annoyance.
April 26 and definitely NOT fixed. Temporarily switched to Spark, but that has issues of its own. Would prefer a working Apple Mail.
Seems there are reports that Apple has coded a “fix” into the next Beta
Seems to be fixed after the OS X 10.14.5 update. However when you first start Mail after the update, you'll have the little squigglies that indicate you're offline. Clicking on them will bring the account online (you have to click on each one in the accounts pane).
It's been 4 or 5 hours since updating and so far so good.