I've just restuck mine with two full length strips of Heavy duty black stick on tape by Velcro. This is exceptionally strong and can easily cope with the outdoors.
At 2 inches wide, the tape will fit nicely along the top and a second strip along the bottom. It is so strong when properly pressed together it takes one hell of a tug to pull the plate off the cars bodywork. The adhesive is far stickier than I have personally seen on double sided foam tape.
velcro-solutions.co.uk
I got mine from Amazon in a 2.5m pack .