Hmm. You know... that does sound like a serious issue, honestly.
I say this in spite of you saying:
checkdsk doesn't find errors, and it shows as "Healthy" in disk
I know this might be inconvenient, but over the course of the next two weeks, make it a point to use that external-drive on another computer as much as possible.
The reason for this is that depending on how much it behaves / misbehaves over the course of the next two weeks, you'll have some idea of how serious the problem might really be.
To wit, if you have the
once in a while (1 time a week), I get the error "An error has
occured. The destination you have specified does not exist".
phenomenon occur once or twice during those two weeks, you'll know that the problem might be with the drive and/or it's connection-cable, rather than just the computer it's presently connected.
Also, if you're able, I'd strongly suggest running various disk-scans and tests that the software program called Hard Disk Sentinel offers.
The website for that program is http://www.hdsentinel.com/
I've been using it as an alternative to 'Windows chkdsk' (or, whatever it's now called... I'm talking about the 'error-checking' tool that's displayed in the following two image files) for some time now and have been quite satisfied with ther results.