A HDD sleeping is different than the computer sleeping. Typically with SSD's people suggest disabling hibernation mode since that creates a system file the same size as your physical RAM. Are you sure you disabled HDD sleeping?
My guess is that your HDD is going in to sleep mode and waking up. Considering it shouldn't be possible to break a HDD by putting it through start/stop cycles (unless you are abusing it) it doesn't really matter and it is saving electricity.
S3 is a low power state. It might be a default in the bios. There are also some more and less aggressive states.
It keeps the ram alive in a low power state and turns most things off or down.
In the bios you might also see some options to allow certain events, like a keyboard to wake up.
You might turn off wake on lan event to stop unexpected wakes.
In ccontrol panel/power options/change advanced power settings/sleep
turn off allow hybrid sleep. That writes contents to a hard drive before going to sleep.
Windows power settings have the settings for putting the HDD to sleep after so many minutes of inactivity (or never). I think mine is set to something like 20 minutes. There really is no reason to disable it. Especially since you have a SSD as your OS drive.