The app has a preset for @web.de, taken from their help page, and it's IMAP.
- You may want to try changing security type from SSL / TLS (strict) to SSL / TLS (accept any). To do this, tap Manual when setting up the account.
- Maybe change the actual logins (on the incoming / outgoing server setup screens) from full "user@web.de" to just "user". Some servers are particular about it.
- Maybe try their web mail, maybe they want you to re-authenticate there... Gmail seems to need this from time to time, maybe other mail services do too.