Do I Need To Repair My External?

I see that this is a pretty common problem, but my External is no longer showing up.
But, it IS showing up in Disc Utility.

The External seems to be working fine, it's lighting up, you can feel it running, etc.

The problem, I think, is that it was randomly ejected improperly. Nothing I did, it just happened, and I got that pop-up warning me about ejecting it the right way from now on.
I don't know how it ejected.

Anyway, like I said, I can only see it in Disc Util, but have no access to the content on it.
Should I repair it, or verify it, etc?

Will doing this delete what's on it? Or does it not matter at this point, is everything gone?

With the drive connected, select in Disk Utility and run Repair Disk and see what is reported. Sounds like the drive may have been corrupted. If Repair Disk does not do the job you have to consider wether worth spending about $100 on Disk Warrior, tech Tools Pro etc.

This is what I got when I "Repaired"

The drive is corrupt - which is basically what the "Invalid Node Structure" is telling you. Disk Utility is a watered down utility which can repair file and folder errors but it chokes on the more serious errors. Disk Warrior could probably repair it but it costs $99 to buy. How valuable is your data?

Alas only two options. Outlay the $99 for a repair utility or use the cash for a new hard drive. If the information on the drive is critical, Data Rescue 3 may be the go but another $99!

If the external was used simply for backups cut your losses and buy a new drive.