External hard drive issue

I have been using a 500 Gb Iomega Ego HDD (USB) to back up my MacBook Pro ( 15" mid 2010, Processor 2.66 GHz Intel Core i7, Memory 4 GB 1067 MHz DDR3) for some time. Occasionally the Mac reported removal of the HDD during a backup session, when it was still connected to the USB port. Usually I would just restart it and redo the backup session.

This time the Mac doesn't show the HDD in the Finder/Desktop. Disk utility can see it and reports no problem except when it comes to ejecting the HDD. At this point it reports that some files are not closed.

Is there a way of resolving this?

You can try repairing permissions but it sounds like the iOmega is having problems. Run Disk Utility verify and repair to see if it shows any errors on the drive. A backup drive has to be reliable otherwise there is no sense using it for backing up so be sure to thoroughly check the drive. If it shows errors or keeps acting up, replace it.