How often does Android 8.1 ask for a password instead of a fingerprint? I use fingerprint to unlock my phone (Nokia 6 TA1033, upgraded to Oreo 8.1, not rooted). Sometimes it doesn't let me use fingerprint and asks for a password instead "for better security". I can't predict when this happens. Is there a way to prevent this? Like maybe unlock with a password on every nth wake-up so that I don't have to type the password in an uncomfortable situation?

Sometimes it is just really inconvenient to type the password, especially when your password is long. Also I believe in public places it is better to unlock with a fingerprint because then no one can see what you type.
On stock Android, a backup authentication method is required after 5 failed attempts, or 48 hours since the last time that backup authentication method is used. 

Using a screen off app will trigger this immediately, as that's how they trigger the screen off.