Remove the vinyl and stick it to some scrap backing paper for now. Get some 3M Primer 94 and brush it on there, let it dry. Now, reinstall your graphic carefully and post-heat it for extra grip. Use some 3M edge sealer also if the edges still aren't happy.
Or, get a (sample) roll of Arlon DPF8000 and print that little strip on it and apply it to the rubber gasket. That stuff will stick to it or anything else.
Tell the customer that there is no guarantee on that strip (no matter what vinyl you use) and when you have a chance go ahead and run a little replacement patch for if/when it does fall off.
When it falls off, have him bring it in and put the patch on the same way again.