Kirby is right in that any uncashed checks are subject to various unclaimed property laws. However, it is not just Illinois that you have to be concerned with. Each US state (plus Puerto Rico, Virgin Islands, DC and Guam) and some Canadian provinces have their own unclaimed property laws. Under US Supreme Court guidance, it is the payee's state that has the rights to collect the amounts as unclaimed property. So, if you have a check with the payee address in say Georgia, you would have to remit those checks to Georgia and not Illinois. Each state has varying penalties for non-compliance, including criminal penalties in certain circumstances. The states have gotten aggressive with audits as well. They use multi-state contingent fee auditors to go after companies that are not in compliance with the law.
I would definitely be concerned about your process. While stale dating in and of itself is not wrong (actually good, because you do not want the bank honoring old checks), you do need to ensure that your processes account for these uncashed checks and handle accordingly. Some companies put them in a liability accrual account until they are dormant under the appropriate state's laws when they are reported. Other companies leave them on the outstanding check list until they are dormant. In any case, if the payee comes back to you before they are reported, the amounts should be available for them, but a new check would need to be issued.
Here's another kicker - state unclaimed property laws also say that statute of limitations don't apply. So if your contract says that the payee has three years to claim and the payee never claims the money, the amounts may still be reportable as unclaimed property. Delaware, the state of incorporation for approximately 1 million entities, audits back to 1986.