"connection to server failed" ... over and over and over again... grrr.

for the last several days when i try to check my apple email via icloud - either on my phone or laptop - i get some variation of the "connection to server failed" error message. I've updated software, logged out, back in, rebooted, all that... and it keeps failing multiple times a day, then eventually fixes itself... only to error again. i've checked the apple outage page and it says all systems should be working. anyone else having this issue and/or know how to fix it? super frustrating, please help!