Why is shrimp rubbery after reheating? How can I prevent this?
I agree with @Joe. It sounds like you are heating too much and overcooking the shrimp. Once things like shrimp are overcooked I am not sure that there is a way to make them tender other than to cook for a long time, similar to slow cooking. With squid the rule for cooking is less than 2 min or more than 20 min to ensure tenderness. 

I think your best bet is to heat slowly and monitor as much as possible to make sure it is warmed but not heated fast so that it overcooks.

In the microwave I would spread the shrimp in a single layer on a plate and using a low power setting, heat in perhaps 20-30 second increments, testing for warmth after each step. You could play around with time and power settings to see what works best for you. The key is to make sure the shrimp do not get too hot, so make sure you turn them and shuffle positions on the plates.

You could also try heating in an oven, covered with foil at around 80-100 C for about 10 min (this is a guess on time, it will depend on the size of the shrimp).