We have 4 LaCie drives which have this sort of problem intermittently. It’s very frustrating and because of it we won’t be buying any more LaCie drives. The problem we’ve found has been most often relegated to the Power Supplies. If you notice, they probably hiss when plugged in. With ours, the hissing has gotten worse over the months until the drives no longer show up in finder. They spin up and sound like the heads are accessing content, but it never shows up.
Basically the only solutions we’ve found are to either replace the Power Supply (works in most cases) or show a little TLC. Our best TLC solution has been to turn on the drive an allow it to get to it’s “stopping point” where it’s not making any more progress. Then quickly turn the drive off and on again while it’s still spinning. Sometimes it takes multiple tries to get this to work, but it eventually does.
We’re in the process of moving all our assets off of those LaCie drives to a NAS Archive and then we’ll likely dismantle the LaCie’s and use the bare drives as hot-swaps in our Server storage. I really don’t think it’s the drive, but likely the controllers or the Power Supply in all those cases.
Regardless, best of luck retrieving your data.
P.S. I’m assuming you’ve already tried disc recovery software? Software will likely recover your assets as long as the drives themselves are not physically damaged. I don’t have any personal recommendations, but perhaps others do. The fact that you can see it in the System Profiler leads me to believe it should be recoverable somehow on your own without dropping a ton of money on a professional clean-room service.