Which Hori Stick is it? A Fighting Stick 3 or a Real Arcade Pro (1, 2, or 3)?
Also, are you plugging the controller into the USB port after the system is powered up or do you plug it in before you power the system up?
I have a 60GB PS3 myself and haven’t noticed this issue with any of controllers I have but I always plug the USB-corded controllers into the system before powering it up. Anything that I use an adapter with always gets plugged in before I power the PS3 up. I also disconnect the controllers after powering down the system first. The official wireless PS3 Dualshock/Six Axis controllers seem to be amenable to being plugged in or taken off USB connections during battery regeneration cycles. This may not be true for third party USB hardware devices, though.
I don’t know if that affects how the system detects the controller to be honest but it’s always better to be safe than sorry. Past generation systems usually recommended having all controllers you were going to use be plugged in first before powering up and to never remove a controller while the system was on.
A lot of USB devices aren’t just “plug-and-play.” With Flash drives, for instance, you have to eject them first before you remove them from a USB slot. External hard drives have to ejected, too, before they can be safely powered down and removed from USB interfaces.
With any number of USB devices like the ones I described, you risk corrupting saved data and losing it or interfering with the software that drives the hardware if you prematurely remove it.