Firefox 5 Beta will not check for updates from an account with no administrator privileges and will not prompt for administrator privileges to apply a downloaded update

I cannot get Firefox 5 Beta to check for updates using an account with no administrator privileges. Firefox 5 Beta downloaded an update (from Beta 2 to Beta 3), and now there is an Apply Update button in the About Firefox window that will not do anything, even after the update is properly applied from a different account with administrator privileges.

I am using Windows 7 Professional 64-bit. I typically use Firefox from an account with no administrator privileges and provide administrator credentials only when prompted to install or remove software.