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The IL security deposit laws, as you correctly point out, only specify a mandatory return timeframe of 45 days if a landlord owns over 5 units. So the fact that you only own 2 units would take you out from under that requirement and put you under the general contract law principles where you have a good faith duty to return any deposit or make any claims within a reasonable time. Statutorily, under IL law, you would have up to 5 years to come after the tenant for any damages to personal property.
So I think that as long as you send him an itemized invoice of any deductions within a reasonable time after he moved out and you had repairs made, then he will have a hard time convincing a judge that you are violating any laws here.
As an aside, in addition to being an attorney, I have also been a landlord for over 26 years but I tend to stick to a 30 day time limit for my own properties...