If the device is plugged in but left idle for about 20 minutes or longer, it will go into low power mode. You can wake it back up by pressing the pairing button until the light comes on and starts blinking again. Or by unplugging it, waiting a few minutes, and plugging it back in.
If this doesn't help, click the following link to see if you can identify what's going on with your drive, it also has suggestions for how to fix it. Chase stutters, jitters, or just doesn't work
If none of the above help, email support@swiftpaws.com with a detailed description of the problem - including any error messages you are getting - and mention everything you have tried so far to get it going. Send pictures or videos of the problem to help us troubleshoot the issue.