Our login password does not work, and we do not know where the reset emails go.

We still have control of the hosting panel.

Any suggestions for someone we could hire to either copy it, and republish it, or how to get around the log in?

If you have control panel access, you should be able to either access the SQL db and add a new root access or change the existing PW, and/or use phpMyAdmin and reset it.

Is this due to simply forgetting the PW or did someone you hired to publish/maintain the site become "unavailable"?

Maybe the account owner (the person who pays the bill) could check with the host.

Often there are two different login/accounts (admin and tech) and the admin account might still be OK?