As my previous post, please send your domain (suffix after @ of your sign in address) to me in PM(Private Message) so I can further help you check your DNS records.
Moreover, please check if you can log in by manually entering the server address: Click options on the sign in page>Personal>Advanced>under Manual configuration enter sipdir.online.lync.com:443 in both internal and external address> restart Skype for Business and check if the issue persists.
Besides, I'd like to gather following information to better help you.
1.Please collect a screenshot of the error message if convenient.
2.May I ask what is your Skype for Business deployment? Are you using pure online service or you have hybrid environment in your organization?
3.Do others in your organization have the same issue?
4.Please check Skype for Business version. Open another Office app like Word>File>Account, it's like Version XXXX (build XXXX.XXXX).