SharePoint mapped as network drive no longer works

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

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

I work mostly via VPN, so on login the drives show as disconnected. Upon opening the drive for the first time per session, the connection would get established and I was able to browse the site contents.

This has worked until recently, when I started getting an error message when I tried to access the drive (by double-clicking the disconnected drive in Explorer). The message reads:

An error occurred while reconnecting S: to
https://sharepoint.mycompany.com/sites/1234
Web Client Network: The network path was not found.

This connection has not been restored.

I have tried removing and re-mapping one of the two drives, which fails with the message:

Error code: 0x80070043
The network name cannot be found.

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

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

What gives?