Why is "my passport air" suddenly not coming up as recognized by my macbook air? The light is on and it is vibrating as it usually does
Open System Information and check the USB bus to see if the drive is recognized on the connection level. If not, you need a new cable or a new drive or a USB port repaired. Try different ports to get a good USB connection.

Then, you need to use Disk Utility to see if the drive has problems. Once you've verified the USB connection is working, then open Disk Utility and click to unmount any drives using that USB connection (eject removes them - unmount allows diagnostics to finish or run).

At that point, you should be able to let the system finish checking the drive and optionally run the verify command.

Once you have a more specific failure, post a new question with details on what your situation is.