Suing and winning are two different things. High chance of them suing, but very little chance of them winning outside the Northeast Corridor or Californistan. Limitations on how far someone is supposed to pursue a thief would be purely a matter of store policy in almost all of the US, not an actual legal limitation. The ambulance chasers would claim that the violation of such a policy (If one is in effect there) amounted to negligence, but there are several possible defenses to that.