Mount and repair external hard drive with command line tools
Yeah, if Disk Utility is telling you it's time to backup and erase then it's not looking good. Perhaps other disk repair utilities can help? But you might just want to heed the warning and backup and erase.  :)

You can force unmount volumes but you can't force mount them. Using the command line, get the device name:

diskutil list

In my case, it's disk2:

diskutil mountDisk /dev/disk2

Or:

diskutil mount /dev/disk2s2

You can run a repair like in Disk Utility, in this case you'll want to include the slice number (disk2s2):

diskutil repairVolume /dev/disk2s2