I have a Seagate USB drive that was doing exactly the same thing; going into a sleep mode after a period of inactivity. The sleep mode wouldn't be a problem if I was just trying to access the drive myself; it wakes up on its own when it detects access, after a few seconds of lag. The problem, as you've identified, is that the Terastation/Linkstation backup utility doesn't wait long enough before assuming an error, and the backup fails.
There is a good solution. The solution is to go to Seagate's website and download the "Drive Manager" utility. Then plug the USB drive into your PC via USB (temporarily), start up the Drive Manager utility, and use the utility to disable the USB drive's sleep mode.
Now you may disconnect the USB drive from your PC and plug it back into the Terastation/Linkstation. It will remember the configuration you just set. Now with sleep mode disabled it will always be available for backups from the Tera/Linkstation.
This worked great for me. My LinkStation Live 320 backs itself up nightly to the Seagate FreeAgent drive with an incremental with deletes backup.
Before I discovered this Drive Manager utility I thought of another solution that would also work. Let's assume you have not disabled the sleep mode. Set a backup job to back up a very small folder; it could even be empty, or could contain a small file. Set the backup job to ignore errors, and set it to run five minutes before your real backup job. This should trigger the drive to wake up, and it will still be awake when the real job runs. The only problem is that your backup logs will be full of error reports, which isn't ideal in my opinion. But it ought to work.
I believe disabling the sleep mode as I discussed earlier is a better solution though.