Refrigerating after reheating?
Same answer as always:  you don't want to eat any perishable food or food for which any part has spent more than about 4 hours cumulative over its lifetime in the danger zone (40 - 140 F, 4 - 60 C).

Do you know how the pizza place treated the calzones before you even received it?  It may have been sitting on a shelf at room temperature for an hour or two at the store before you ordered it, in addition to the transport time when you took it home, and all the times as you heated and cooled it when it was in the zone.   

In general to reduce the quality degradation, and the amount of time food ends up moving through the danger zone, you normally only want to heat up the portion of food you intend to eat, and leave the rest refrigerated.

See also:  https://cooking.stackexchange.com/tags/food-safety/info