OS 10.9.3 Seagate External Drive Won't Mount
I don't know exactly what build changed the mount behavior of OS X, but there are times when you will connect the disk and the OS will no longer mount it until the system has finished the file system check (fsck). There is no visual notification that an extended check is being made, so you have to rely on Disk Utility or the Activity Monitor and actively look to see if a check is in progress.

Connect your missing drive again and then, open activity monitor and select the CPU tab if needed. Then search for fsck - if you see a process with that name (or similar fsck_hfs, etc...) then the system has decided to check the contents before it knows to let you have read-only access to the drive or read-write access.

If that's not the case, then you may have some odd corruption that requires a repair of the drive structure (in your case select the main "Blorp" and not the indented "Blorp" in the left pane of the Disk Utility window. The dimming of the repair button is indicative of a process already running to check/repair that volume.

Most cases, this is a check that could take some time, but often is done within 5 minutes or less and not something that happens every mount but after another problem was detected or logged to that drive such as an unclean ejection or force eject.