I am using an external drive for a time machine backup. It has disappeared from the desktop. How do I get it back again?

My time machine backup disc, which has been working ok for a couple of years has suddenly disappeared from the desktop. The time machine program tels me it is unavailable. I have checked that the drive is working by booting up in Windows. and Windows can see it and read it ok. What has gone wrong, and how can I fix it?

I have tried unplugging it and reconnecting, but it is still apparently not seen by the system.

I could use Windows to reformat it, and start again, but this would loose all my previous backups, and I've no guarantee that the system would notice it even then.

Has anyone any ideas?