WD 2TB My Passpost does not show up on MBA

Either the enclosure or the HDD itself could have died.

You could remove the HDD from its enclosure and try it in a different one (USB <> SATA adapters can be had for 10 €) and see, if that works.

If that does not work, you have to contact WD about your warranty. I do not know, what WD's warranty says about data recovery or similar, but I presume, that it is not covered and they will probably just send you a replacement.

If you have an experienced computer repair store nearby, you could also employ their help.

And for the future, as backing up is important:

I have one 500 GB HDD for my photographs (digital and analog), libraries and editing documents, one 500 GB HDD with my personal video footage in an editing friendly format.
Both 500 GB HDDs get backed up to one 1 TB HDD via CarbonCopyCloner.
And that 1 TB HDD gets backed up to another 1 TB HDD via CarbonCopyCloner.
Therefore I have three copies of my important data.

Click to expand...

Just bought exactly one of these the other day and it works fine for my MBA. I store my entire Aperture library on it backed up to a 4TB drive at home.

Go into Disk Utility and see if it's picked up the drive but is showing as unmounted. If so, try to mount it, also try to Verify Disk.

I know it might be obvious, but have you tried a new lead for the HDD in case it's the cause of the failure.

The other option have you tried some other device in the USB, in case the port has lost power

I stay well away from Western Digital products.
their controllers are 'integrated' so recovery of data is nigh impossible when they stuff up.