My prayer to Our Lady of Perpetual Adhesion went unanswered 
(Turns out the one thing E6000 won’t glue is the LED strips’ silicon sleeves. Double sided tape to the rescue…)
See also http://thistothat.com/
Silicon isn’t easy to glue to unless you roughen up the surface a bit. Even then, it’s meant to release (which is why some processes use silicon as a release agent.)
If you think silicon is difficult, try PTFE…
An arduino tutorial has this adhesive noted for being good at sticking to silicon sleeves: Permatex 66B adhesive
Devcon makes a silicone adhesive which works great for sticking silicone to things. http://www.amazon.com/Devcon-12045-Premium-Silicone-Adhesive/dp/B001005TX2/ref=sr_1_8?ie=UTF8&qid=1401231315&sr=8-8&keywords=adhesive+silicone. I’ve gone through about a gallon of this stuff in making and waterproofing my led mermaid tail.
I Have used the Permatex 66B. It will let the Silicon sleeve stick to the Outside rims of my shoes. I used it to stick just about anything to any surface. Also note that it isn’t a glue. So you could spend time to slowly peal it off the material you use this adhesive on.