A few years back, our home was struck by lightening and we lost our computers and a lot of other items. What wasn't backed up and stored unplugged from the wall was lost. We paid a service $95 dollars to retrieve info on one machine. A few days ago my lap top mother board fried. Instead of paying another $95 dollars to try to retrieve what wasn't already backed up, I bought a Sata docking station for $35. It was easy to remove the lap top hard drive and recover the unsaved info onto my desk top. Now for $35 I have my info and a cheep portable hard drive for future use. These docking stations are available for almost all hard drives. If your not a computer geek, you may not have known about this alternative.

Here's a different angle, but similar problem. I have a 1TB Western Digital external drive (backed up, fortunately). In the midst of trying to rearrange my work desk, I accidentally knocked the drive off its shelf. It fell about two feet or so before hitting the floor and it didn't sound like a very hard hit. However, the drive began to de-boot.

If the drive is not powered or energized and you drop it you probably won't damage it. Damage occurs when your drive(s) are running, and you drop it while you have energy running through it.
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After checking to see that my backups are fine, I reformatted the drive, setting the software to block any damaged sectors. After this, the drive began to work - for a while - and then started to dropping off-line.

If you don't mind me saying so, this was your first mistake. Any sign of a damaged or dying drive and you should IMMEDIATELY replace it, especially if you can still run it and collect data from it.
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Rebooting the computer would bring it back up, but after a time, the drive would again un-mount itself. I have found some very nice prices on bare drives and I've wondered whether it would be feasible to get a new drive and put that into the old enclosure. And whether I could put, say, a 2 to 4 TB drive into an enclosure that once held a 1 tTB drive. As in, is there something in the enclosure's electronics that limits it to a particular size drive. (BTW, this is NOT a boot drive, just a data drive)

Here's a different angle, but similar problem. I have a 1TB Western Digital external drive (backed up, fortunately). In the midst of trying to rearrange my work desk, I accidentally knocked the drive off its shelf. It fell about two feet or so before hitting the floor and it didn't sound like a very hard hit. However, the drive began to de-boot. After checking to see that my backups are fine, I reformatted the drive, setting the software to block any damaged sectors. After this, the drive began to work - for a while - and then started to dropping off-line. Rebooting the computer would bring it back up, but after a time, the drive would again un-mount itself. I have found some very nice prices on bare drives and I've wondered whether it would be feasible to get a new drive and put that into the old enclosure. And whether I could put, say, a 2 to 4 TB drive into an enclosure that once held a 1 tTB drive. As in, is there something in the enclosure's electronics that limits it to a particular size drive. (BTW, this is NOT a boot drive, just a data drive)

That is another "maybe"... Whether or not your new drive will work in the old enclosure depends on the maximum size the enclosure is designed to support. On one hand, the MFR may have used the cheapest enclosure that would do the job in which case it may just support up to 1TB...You could try it and see.....The good news is that these enclosures are not expensive and can be found as low as $10-$20...So even if you buy a bare drive and it does not work in your enclosure, you can get one that WILL work very easily...

"USB's limit is the limit of its mass-storage class (MSC) spec. This spec is in turn based on the SCSI transparent command set. (See also http://en.wikipedia.org/wiki/USB_mass_storage_device_class#Device_access). Looking at the SCSI read commands (http://en.wikipedia.org/wiki/SCSI_Read_Commands#Read_.286.29) you can see that there are several versions of the API. The oldest supports 21-bit block addresses (and a 1GB limit), a later version supports 32-bit LBAs (imposing the 2TB limit many cases have today), and the latest has a 64-bit LBA which will impose an 8ZB limit (that's 8 giga-terabytes!). "