Unable to open Web Project '/'. Not found.

I'm attempting to publish from VS to our hosted server, as I have been doing.
However, recently, this has failed. When I do a Project\Copy Project
operation, I get the message I put in the Subject line. I do have FPE
configured on the site to which I'm publishing, and this has been working.

I've noted that in the properties for the site, the ISAPI Filters tab has
one item, fpexedll.dll, with a priority of *Unknown*, and this is different
from other sites where I have FPE installed and it is working. I've
restarted IIS; I've uninstalled FPE on the site, rebooted the system, I've
deleted the site and rebuilt it from scratch, and nothing changes this.

I need to get this working; are there any suggestions about what is going on
and what I can do?