Firefox’s Proxy Auto-Login Option Needs an Existing Saved Login
Separate permission to save a proxy login from permission to reuse it silently, including previous failures and private-mode limits.
Firefox’s Do not prompt for authentication if password is saved option reuses a saved proxy login. It cannot supply an account the profile has never saved.
Check that password saving is permitted for the profile and authentication origin. Complete the proxy challenge with the intended account and accept the save prompt when offered. Then enable silent proxy login in Connection Settings if wanted.
The corresponding preference is signon.autologin.proxy. Firefox requires an existing matching login. Its authentication code also checks that the previous attempt did not fail and permanent private browsing is not active.
A rejected password can therefore bring the prompt back. A changed proxy endpoint or authentication realm can also prevent an older saved record from matching.
Check saving, matching and acceptance separately. An auto-login preference cannot override a managed restriction on password storage or make an invalid account succeed.