How do I turn on Face ID or fingerprint unlock?

Go to Settings → Security and switch on Unlock with Face ID (or Fingerprint, depending on your phone). The wallet must be unlocked when you do this.

It turns itself off, and you unlock with your password instead, when:

• you change the wallet password, or
• you add or remove a face or fingerprint in your phone's settings.

That is a security measure, not a fault. Switch it back on afterwards. You can always unlock with your password.