Clicking “Remember Password” does nothing

Question

In Firefox on Mac OS X, when I click the "Remember Password" button on some sites, nothing happens — the popup does not disappear, and the password is not remembered.

So far I've tried:

• I tried restarting Firefox in Safe Mode; no change.
• This bug report suggests enabling signon.debug in about:config — I'm getting this error message:

Error: NS_ERROR_XPC_JS_THREW_STRING: 'login values can't contain nulls' when calling method: [nsILoginManagerStorage::addLogin]
Source File: resource:///components/nsLoginManager.js
Line: 394

• This similar Super User question suggests reinstalling Firefox.app. I did; no change.
• The Password Manager Troubleshooting Guide suggests deleting my profile's signons.sqlite and key3.db, but after restarting Firefox, it still doesn't remember passwords.
• Updating Firefox — Firefox 15, 16, 17, 18, 19 all exhibit the problem.

What else should I try?