External hard drive not recognised by MacBook Pro.

First off if you notice issues with an external drive like you describe that is the drive trying to tell you that it is failing. Hope you have a backup.

If it is not showing up in Disk Utility you could try rebooting the Mac, with the drive attached, a time or two. Power cycling the drive, unplugging it and plugging it back in, all of which might get it working or might do nothing at all.

If you can get it to mount and there is nothing you need on the drive try re-formatting it. If that fails then you definately have a bad drive instead of just a corrupted one.

If you have a third party disk repair utility (I like DiskWarrior) and it will see the drive run that.

Honestly it sounds like the drive is dying and needs to be replaced, either under warranty or by buying a new one.