I don't think your customer is really "kiting" but they're probably engaging in a case of issuing worthless checks (maybe). The customer would be kiting if the deposit they made with you was in the form of a check drawn on another financial. Have the businesses who accepted these checks that were stopped contacted your LP department to talk about what's going on?
I also agree with bwest, how can this person afford the fees? If you feel uncomfortable with the situation you can always close the account. You're under no obligation to maintain any account relationship that your company doesn't feel is beneficial.
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Opinions stated are not necessarily that of my employer.