B737 Captain reported the door handle on the forward service door moved out of closed position several times during cruise. Flight diverted and landed safely.

Narrative

After departing ZZZ; soon after leveling off at FL280; the FWD service door light illuminated. We referred to the Flight Manual; which states that if the door handle is not in the closed position; then to divert to the nearest suitable airport. The flight attends reported that the handle was not in the closed position; and that the end of the handle was raised about 4 inches from the closed position. After they moved the handle to the closed position; it would remain briefly; but then return to the same raised position; and the light would illuminate. This sequence was repeated more than once. We worked with ATC to enter holding and descend to 10;000 ft MSL. The captain conferred with dispatch and Maintenance Control via ACARS. After discussions with the captain; we agreed that our condition met the definition of the handle not being in the closed position and therefore the applicable flight manual guidance was to divert to the nearest suitable airport. ZZZ and ZZZ1 were about the same distance from our location. A thunderstorm had moved over ZZZ; so we chose to go to ZZZ1. After landing; maintenance initially informed us that they could defer the issue and we could fly to ZZZ2. They felt it was probably an indication problem (maybe wiring). The aircraft had had a similar indication on a previous flight approximately 4 days earlier and the flight had continued to the planned destination. However; the writeup for that occurrence didn't describe the handle position during flight. After further discussions with maintenance; they agreed that an indication problem alone would not explain the movement of the door handle. Maintenance agreed to conduct a test involving pressurizing the aircraft and testing the handle for movement (and also checking handle tension). After the passengers were deplaned; the test was conducted and the handle movement was confirmed. I believe maintenance also reported that the door handle did not pass the tension test. About an hour after the test was completed; crew scheduling called and removed the captain and me from the trip because of the time required to complete the repair.