iCloud email account goes offline repeatedly in Mail

During the day my iCloud email account stops working 4 or 5 times, with a triangle beside the inbox and "account" error in top right of the main window

Turning the wifi off and back on resolves it. But I can't fix the issue:

- quitting and restarting Mail does not work

- choosing to put account online doesn't work

so far I have:

- upgraded from 10.10 to 10.11- same issue under both versions

- logged out of iCloud in System Prefs, then signed back in

- erased the Mac HD and performed clean install of 10.11, plus signed back into iCloud again

NO change

when the iCloud account goes offline, my other email accounts and webpages work fine.

ANy ideas? Thanks!