You said "serum" correct as in blood serum right? If so then thats your problem.
Iodine like most minerals is primarily stored in tissue NOT in serum. A serum Iodine test, like most serum tests for minerals is worthless. You need to do a urine loading test to see how much your body is excreting.
The body tries to maintain serum numbers regardless of tissue stores so that it can get it where it needs it fast. Serum numbers dont generally drop below lab range until a raging deficiency is taking place.
Iodine is water soluble and IF the body is sufficient in Iodine it will excrete whats not needed. However, it would make sense that if your tissue is NOT sufficient your body is not just going to pee it out if it doesnt have to because your tissue needs it. However other halogens can prevent the uptake of Iodine so its going to take some time for those halides to get flushed out to make room for iodine.