When running a Fedora 18 system booted by EFI, do not run grub2-install. It will claim success, but it breaks the Fedora grub-efi boot system.
The file /boot/EFI/fedora/grub.efi is installed by the grub-efi package. If you do want to reinstall it, use yum reinstall grub-efi. (To do this from a generic rescue system, you can do this after mounting and chrooting into your installed Fedora system). Fedora grub-efi uses the config file /boot/EFI/fedora/grub.cfg (presumably generated by grubby). Fedora on EFI won't generate a file at /boot/grub2/grub.cfg. Running grub2-install will replace grub.efi with an image that tries to read /boot/grub2/grub.cfg, and will therefore fail.
grub2-install installs an EFI boot entry for grub.efi. However if you have not disabled Secure Boot in your Windows 8-certified firmware, this entry will fail to boot. You need to boot shim.efi instead (ignore shim-fedora.efi, I'm not sure exactly what that is). See below.
You can lose your EFI boot entry for Fedora if your firmware settings are reset. (Manually, or by firmware upgrade, or because firmware is buggy - the latter has been reported in the wild). Here's how to manually create an EFI boot entry for Fedora with secure boot:
$ sudo efibootmgr -c -L Fedora -d /dev/sda -p 100 -l \\EFI\\fedora\\shim.efi
This example uses partition number 100 on the first standard disk recognized by linux. You should adjust the options -d /dev/sda and -p 100 to identify the filesystem which Fedora mounts at /boot/efi. This is an EFI system partition. The Fedora installer will have created a dedicated ESP for your Fedora install to use, separate from the ESPs used by any other operating system. (This is different from Ubuntu and OpenSUSE).
Note the efibootmgr command requires that you run it from an EFI-booted system.