I suspect that an update/patch/sp somewhere along the line has broken SharePoint somehow. I've been fighting all week trying to figure out why certain site settings pages work for a little while and then stop loading, throwing a 403 error (forbidden). If they never worked, then I'd assume that the permissions somewhere needed fixing. But if I do an IISReset, the pages execute fine.
For a little while.
And then they stop. For no obvious reason.
Finally my boss Ignacio (who was also looking into the problem) found a reference to this MS kb article that doesn't mention this issue specifically but seems to fix the problem. (See here.)
If I get any better information, I'll share ASAP.