I checked "Belarc" for the computer but couldn't find a listing for the Power Supply. The only visible tag on the power supply is DP/N OM1J3H.
Assuming you've not build it yourself then
- It's common practice to put the minimum rated power supply in with the case - running a large number of drives is likely to be really pushing the design of it.
What I have a question about is what part of a USB circuit draws significant wattage. Each of the HD caddies has it's own power supply which I assume handles the spin part of the drive but not the bits and bytes. If the wattage drawn by the PC board and caddy circuits is small (compared to the power supply wattage) then the problem might be in the USB path and voltage drops along the way rather than wattage
At this point I have disconnected the caddies and intend to use them only when I update backups to them. I also shortened up the USB cables from 6 ft to 3 ft. I'm using the 3 internal HD drives for daily work.
That's quite true - but you'll get a small power drain from the USB controller itself, though admittedly not actually that significant - It should be less than a couple of watts.
What could (in theory) be happening is that as your main PSU is being pushed out of limits, and it's not a top-quality one, your 5v rail may be struggling - this would cause problems for USB. Short of getting a PSU tester (though they're about $10 from your local favourite computer supply store), you could try plugging in a USB mouse and seeing if the light on the bottom shines consistently.
Generally though, getting a nice big PSU is something you could look at - it'll actually draw less power than a lower rated one at the same output. Either that, or it's multimeter time and working out exactly what's being drawn.