DD Rescue isn't really an imaging program as such, it does a straight
byte for byte copy from one HD to another - so the destination drive
has to be as large or larger than the source one even if there's only
a small part of the original drive in use. Imaging programs will take
the used space on a drive only, and also compress this so that you can
take an image of a 500Gb drive that's only got 60Gb used onto an 80Gb
drive - ddrescue would not be able to do that.

Clone Zilla is a free imaging program that has good reviews though I
didn't get on well with it a number of years ago. It's probably a lot
different now but so far haven't tried it out.

As for the USB to SATA adapter. If it works fine on lower capacity
drives then it *could* be power drain - have you tested it on a HD
that you know used to work fine in it ?

Pardon my confusion of terminology. I think I would lean more towards ddrescue
than an image. When trying to rescue data, does one method have an advantage
over the other?

That USB to SATA adapter (Apricorn Drivewire) has been tested with several
drives. The problematic drives were all purchased within the past year. They
have been of various makes (Seagate, WD) and sizes (500G and 1TB). The 1TB
drives of more than a yr ago didn't have the problem of dismounting, but the
later ones have. Also, I've tested several older IDE drives, and there's not a
problem with them.
I've disconnected other USB devices and have tested on multiple machines and
OS's (XP and 7), but the behaviour is the same on each.
I've re-tested it on a drive(s) known to be good, and it works fine.

To correct the voltage problem, would a powered USB router help, possibly? Or,
is there a good measuring instrument to somehow detect when (or where) there is
an interruption in power supply? Maybe more accurately, an instrument to detect
when the HD's demands exceed the supply?

Data rescue implies recovery of data from corrupted drives and drive
imaging or ddrescue will not do that. All these programs are concerned
with are making a copy of the existing drive contents. The difference
being that ddrescue is a byte for byte copy that can be plugged into
the PC and run just the same as the original drive, whilst imaging is
a method of creating a compressed snapshot that can be restored back
to the original drive ( or a new one ). Most imaging programs now have
the ability to mount the image so that the contents can be viewed and
files copied back to the system without the need to do a full restore.
Data Recovery is a whole different ball game

As for the Apricorn Drivewire adapter, this has its own power supply
so the USB side is only used for data. Connecting to a powered hub
shouldn't make any difference as power draw on the USB side will be
low. It's the power draw of the HD motor through the adapter that's
possibly where these larger drives are falling over but not definite
that that's the cause. Later drives of 500Gb and upwards may well have
4Kb sectors ( instead of the 512 byte sectors that HD's have had for a
long time ) but I can't see that being a cause of them dismounting.

A curious problem that might just mean that your adapter is not quite
up to the job with these larger drives, or wear in the connectors is
beginning to make itself felt. Also does the power unit get hotter
than it used to do ?

Thank you for your reply and for the info on ddrescue vs imaging.

The adapter hasn't been any hotter than previous (on the Apricorn Drivewire).
In fact, the company sent a replacement, and the same problem persists.

I might check out that sector size difference to see if there could be a
problem.