Many system integrators and OEMs buy an annual "Toolkit" license from Rockwell, which does expire each year and needs to be renewed.
Toolkit licenses typically cannot be sold privately; they're a nontransferrable subscription.
Unethical folks can and do bypass or misuse the Rockwell licensing system to sell laptops "preinstalled with RSLogix" that cease to function when the license expires. If you bought that laptop off eBay, that's very likely what you got. A couple guys in Indiana spent a few years in Federal prison for that in 2012.
If it's not a Toolkit license, then the computer might have an ordinary non-expiring permanent license that is tied to its hard drive volume ID or a network port's MAC ID. You can also buy a hardware dongle that provides a portable unique identifier so you can activate your software on multiple computers, one at a time.
Open up the FactoryTalk Activation Manager utility and look for the serial numbers for your software and their expiration dates.