The above fix (deleting the temp files) did not work for me. I had to delete the PageName.aspx.designer.cs file, then right-click my page, and choose “Convert to Web Application” from the context menu.
When Visual Studio attempted to rebuild the designer file, it encountered (and revealed to me) the source of the problem. In my case, VS had lost a reference to a DLL needed by one of the controls on my page, so I had to clean out the generated bin folders in my project.