Windows 7: SharePoint assigned as a network drive no longer works

In the past, I have accessed two SharePoint sites on our company's network by mapping them as network drives. I mean, I added a network drive in the File Explorer to a form URL

https://sharepoint.mycompany.com/sites/1234

I work mainly through VPN, so when logging in, the units are shown as disconnected. When opening the unit for the first time per session, the connection would be established and I could navigate the content of the site.

This has worked until recently, when I started receiving an error message when trying to access the unit (double-clicking on the disconnected unit in Explorer). The message says:

An error occurred when reconnecting S: a
https://sharepoint.mycompany.com/sites/1234
Web client network: The network path was not found.

This connection has not been restored.

I have tried to remove and reassign one of the two units, which fails with the message:

Error code: 0x80070043
The name of the network can not be found.

I can still open the URL in my web browser (indicating that the site is available and name resolution works).

The operating system is Windows 7. The Web Client service is running (started manually). I added the SharePoint site to the Trusted Sites zone in Internet Explorer.

What gives?