Since then, I have been moving all my domains from them to a new registrar.
I missed three. One of which was a .ORG.
Even though they were expired, I was able to transfer them to a new registrar, except for the .ORG.
The .ORG requires an Auth Code to approve the transfer. And, since the registrar doesn't respond to anything, I could not get that Auth Code.
That registrar is/was a reseller for a wholesale registrar, through which the domain was still registered.
I contacted them, and explained the situation very specifically, and the response I get was that I need to deal directly with the reseller or the gaining registrar. Well, the gaining registrar can't do anything without the Auth Code--and they cannot give me the Auth Code for a domain they are not the registrar for! Which leaves the non-responsive registrar.
(Another option was to log into a special page on the wholesale registrar's site, that would give me access to all my domain details, including the Auth Code. But, in order to get into that, I need a username and password. To get that username and password, I need to contact--guess who?--the reseller.)
What the wholesale registrar did not tell me is that I do not need an Auth Code to transfer the domain to another one of their resellers. Since the domain is technically registered through the wholesale registrar, a transfer from one reseller to another is not quite the same as an ordinary registrar to registrar transfer.
You would think the wholesale registrar could have told me that.
In short, I managed to retain my domain name. Fortunately, this one was not yet in active use for a site, so the downtime is not an issue. In 60 days, I will transfer it to a registrar I trust, and avoid this particular wholesaler and its resellers in the future.