The Adhesive on my Vehicle GPS seems to have worn out. What is the best method to fix this problem?

They make some velcro that is incredibly strong by 3M (I think and probably several others now). You can also use superglue, if you want it permanently mounted. If both surfaces are smooth and clean, it will bond anything almost. I have used it in combination with the velcro backing and it works very well. There are also some double sided tapes on the market that are very durable.