Seagate external ejecting problems

I have two seagate 1TB externals, one is a small one that is powered with usb 2.0 and the other one is a bigger one with its own power source . These are both on a new mac mini running lion. The small one i have no problem with. Every time the mini goes to sleep with bigger drive still mounted I will wake up the mini and get that annoying warning saying i didn't eject the drive properly. It is also my Time Machine backup drive, so the way i have been dealing with it is just ejecting the drive every night, or when i go to work. Does anyone have any other suggestions? The drive always remounts when i wake the computer up, but not if i eject the drive before bed. Then i have to restart or unplug the drive and plug it back in. I do not know if i might damage the drive or lose data if i just leave it alone and deal with the warning every morning. The warning says it could damage the drive, I just do not know.

yeah, i may give that a try or may just keep ejecting at night. See today the drive was mounted right when i woke up the computer and seems like a Time Machine backup started.