External Hard drive Icon Disappears

I've been using an Iomega external drive as my Time Machine since I bought my iMac in 2008. Now that I have upgraded to Mountain Lion the external drive icon keeps disappearing and Time Machine fails to backup my files. The Disk Utility does not list the external drive once the icon disappears. If I turn-off and then turn-on the external drive the icon reappears. However, it will eventually disappear again.

I have tried all solutions that I came across on numerous forums and apple discussions to no avail. Any help will be greatly appreciated.

In order to not re-iterate all the things you've tried from "numerous" forums and apple discussions - most folks are going to want to know what you've already tried.

If the drive was purchased back in 2008 and is mounting and dismounting randomly, it's time to buy a new one. Nothing worse than having an unreliable external hard drive as backup.