Is there a limit to the number of attempts to logon to an iPhone 8?

A relative managed to change her password, yet can not input the correct password. She does not want to reset the phone to avoid loss of data (pictures, contacts, messages, etc.). Will the phone eventually stop accepting logon attempts?

By default, there is no limit. One can be set - usually on sensitive business phones rather than consumer devices - where after 10 unsuccessful attempts the phone will wipe itself, permanently.

However, without that parameter set, each successive failed attempt will lengthen the time before another attempt can be made. If you keep trying, eventually the time can become months or even years, so be careful.

There is no way to force an iPhone to let you in. If you really cannot remember the passcode, you will eventually have no choice but to wipe it & start over.
At that point, you will also need to be able to correctly login to the Apple ID that 'owns' the phone to release the activation lock.

See Apple KB - If you've forgotten the passcode on your iPhone, or your iPhone is disabled for further detail.

The max number is 10. After 10 attempts the iphone erases all its data. The iphone also has a sliding scale for how long to wait between login attempts. You can try 5 times pretty quickly but then it'll make you wait 15 minutes, an hour, up to 8 hours before trying the 10th time, i think.

This process has to be set first. Go to Settings on you iPhone and scroll down to Face ID and Passcode. Click this and scroll all the way down and you'll see an Erase Data button. If that button is turned on, then the data will be erased after 10 login attempts. The difficult part is that owner probably doesn't recall setting this. But if the owner is mistaken it could cost all the data.