In digging further into this problem I came across this discussion

https://support.mozilla.org/en-US/questions/1210879.

As user Shadow110 mentioned in the discussion linked above, you can open the sync log be entering about:sync-log in the location bar. After opening the sync log and combing through it, it looks like the request to sync returned a 503 (server maintenance) and I came across these lines

1573264771936 Sync.Status DEBUG Status.login: success.login => error.login.reason.server 1573264771937 Sync.Status DEBUG Status.service: success.status_ok => error.login.failed 1573264771937 Sync.ErrorHandler DEBUG Got Retry-After: 3600 1573264771937 Sync.Status DEBUG Status.login: error.login.reason.server => error.sync.reason.serverMaintenance

So, it looks like the server is down for maintenance and once it's back up sync will start working again.

Did it work out?

Try to disable Syncing. Than enable again Login and sign into your Firefox account.

Sync logins in Firefox for iOS

JoeBello82 said

I’ve verified that my desktop app and iOS app are both updated and using the current version of Firefox sync. I’ve signed out and back in on both devices. I’ve removed my mobile device from registered devices and then added it back. I’ve also uninstalled and installed the iOS app multiple times.