Should Portokalopita be refrigerated after baking?

It's your call.

This cake is from an era before electric refrigerators were commonplace in Greek homes.

Moreover, these syrup infused cakes tend to have good preservation characteristics. If you have a cool, dark place, that would probably be a suitable place for storing it.

Some more recent renditions of portokalopita use less syrup so refrigeration might be more appropriate for these modern versions. If you feel more comfortable refrigerating it, go for it.

Best of luck.