Outlook 2016 doesn't accept password or app password

Your observation is very consistent with mine. It seems in the last couple of days, the prompt happens when I switching from mobile to non-mobile data network, and between one network and another (happened when I enabled VPN and again when I disabled VPN). It seems like MS systems authenticates and grants permission weighing heavily on IP address, so if the device suddenly changes IP address/network, it would fail the new attempts, even if it was previously authorized on those networks. Given competing platform/email system handle the same situation gracefully, it suggest these are MS issues or possibly design flaws with their security protocols.

Note that outlook.office365.com, eas.outlook.com, m.outlook.com, and s.outlook.com are all just aliases for the exact same thing.

From what I've observed when this was happening (has been fine for 2 days for me now), it isn't the settings themselves that make any difference, just the fact that when you change the settings, you disconnect and reconnect, get a new randomly assigned server, and often times that is one of the working servers. Same when flipping between wifi and mobile data etc.

I've gone about 2 days now without a single disconnect on my Gmail for android with EAS, that's with multiple changes between wifi, mobile network, etc.

Anyone still having the issue, can't say whether it is fully fixed or not but you may want to make sure you have 2FA enabled and are using an app password (or modern authentication if the app supports it) and are configured to use exchange activesynch instead of IMAP (EAS is much better anyway).

Worst case may need to delete the account from the device, clear the app cache, delete the device from your MS account (mobile devices are listed under settings on outlook.com), and re-add it. A reboot between deleting and re-adding isn't a bad idea, and generate a new app password (clear old ones if you don't have any other devices using them too).