When the Finder complains that a drive was not ejected properly, that means that your problem is not that the drive is going into sleep mode, but rather that the hardware connection from your drive to your computer is crapping out. Unfortunately, it is impossible for me to say whether the problem is internal to the drive itself, or in the drive's enclosure, or in the cable, or in the port that connects to your computer. Try swapping out the cable that you use to connect the drive, and try connecting it to different ports. If nothing else, this will help to narrow down the range of possibilities. My hunch, though, is that the issue is in your drive's enclosure, since it appears that your drive sometimes reconnects soon afterward, but is considered by your computer to be a second drive with same name (which is why it appends a "1" to the end of the drive's name). But that's really just a guess and is by no means a diagnosis.
If I am right that the problem is with the drive's enclosure, there are likely two options available for you:
1. If the drive is still under warranty, exchange it at the store for a replacement.
2. Purchase a new enclosure and move the drive itself from its old enclosure into the new one.
But as I said, I can make nothing more than a guess at what the problem with your drive really is, so that advice comes with nothing even remotely like a guarantee. It may not be appropriate or helpful in any way, and I accept no responsibility for any negative consequences that might occur to your drive, your computer, or your wallet if you follow it without consulting a qualified technician who has physical access to your drive.