Using Outlook for iOS in business environments for email and scheduling
I am having the same exact problem for about 3 days. It waxes and wanes. Primarlily "can't connect to server" and occasional prompt to re-enter password. Given your completely identical experience and timeframe, it must be on "their" side, whoever they are. Microsoft, Apple or both. I'm not sure if Outlook on the phone goes through Apple's Cloud? I've gone through several things including deleting and re-installing my account. Also worth mentioning is my Outlook On the Web account on my PC is working perfectly and sync's from my iCloud calendar from the phone to my PC are sometimes slower than usual. This needs Microsoft attention.