I think it is because of the much larger size of the iodine atom compared to the other halogen atom sizes. The bond length would be greatly increased and the stability will obviously decrease in that case.
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The Brainliest Answer!
Iodide ions are strong reducing agents. Therefore, Copper (II) Iodide reduces to insoluble copper (I) iodide. Thus making CuI2, CuI. CuI is not stable, so it doesn't exist in solution. It isn't stable because of electrochem and the solubility. 

I hope that this helps a bit
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