I received several letters from people having great trouble trying to get vinyl wallpaper borders to stick and stay put.
It is actually quite easy. The trick is to understand that regular wall paper adhesive will not stick to the top surface of vinyl wallpaper, so vinyl borders over vinyl paper must use a special "vinyl-to-vinyl" adhesive. It says that right on the can.
If most of your trim is up and seems to be holding but there are just a few edges opening up, just use a Q-tip to sneak in a little vinyl-to-vinyl adhesive.
Problems with joints opening up with regular wallpaper? They also have a special "seam repair adhesive" which comes in a small easy to apply tube. Just squirt it in, push it down a bit, let it soak in, then push it down again while wiping it off. Voila.
Thanks for the help from the people at Provincial Wallcoverings in Toronto.