Velociabstract had a post with photos of when he lost or nearly lost the top trim and the photos showed that the double-sided tape had separated from the clip which had been stuck to the upper trim. The trim clips remained attached to the mating clip which is riveted to the car. The same basic principle applies to the top and side trim.
Some tape was still adhering to the trim and some to the clip, the tape appeared thinner than the regular 3M tape. Maybe this can be obtained from a body shop.

I think that 3M VHB double-sided tape is probably the best tape to use, it comes in various thicknesses and the normal 3M double-sided tape which has a foam core is too thick and will not stand up to the harsh conditions.