You are probably loosening/pinching/stretching etc. the power connector cable. If you are using chinese made "Y" connectors to tap off of existing interior power cables, take a look at the pins and sleeves they stick into and see if they are making good contacts.
This has happened to me many times, even when I bought 10 brand new ones. The connectors are just cheaply made and a bit of love from a small flat bladed screwdriver (with the computer unplugged and the "Y" connector unplugged from the computer entirely of course) can help correct the connections. Sometimes the sleeves are too wide or the pins have abnormalities.
Good luck.
(Another thought. Make sure to see what your power supply is rated for. I've slammed 8 HD's in a G4 server. Various old drives that I felt had a few more months of life in them. When everything spins up, the computer can just overwhelm the power supply. I've found that 4-6 drives can be done as long as you do the math and stay within the power supplies limits. You can turn on the let hard disks sleep function in energy settings to lesson the power usage of drives that can be dormant most of the time.)
