I don't have that drive, so I can't comment on that one, but, usually when you see that number get into the thousands (1 sec +) that is a sign.
You can get a SMART attribute change on lots of things, it don't have to be on copying. Usually, when you copy, and something goes wrong, it will trip the reallocated sectors, and on the next access to that sector where it tries to write to it, it will determine if it should swap it out, or keep using it.
It is good to have HD Sentinel running... but, sadly, this and any other SMART readers don't always warn you if the HD is about to die. SMART isn't smart enough to always tell you when the drive is about to die.
If I was you, I would just keep an eye on the HD, and if access times keep getting higher, I would delegate that drive to a scratch drive where you don't care if the content on it is lost.
If you do care about the content, you should be doing backups.