Stable Iodine levels?

I just can't seem to get the Iodine to stabilize in my tank. I use Kent
salt and have tested freshly mixed water and found 0.0 ppm Iodine so I
figured I was starting behind the eight ball. However, I added Kent Iodine
supplements over a few days and got the levels up to 0.04 ppm or so and
though it good for at least a week. I tested after two days and once again
0.0 ppm. Anyone else have this problem? I really love shrimp and crabs in
a tank and want to keep a stable (relatively normal) Iodine level. The tank
is freshly cycled with 50 lbs of live rock. Other water parameters are
fine. TIA -Andy