Hi! I have a couple of favorite adhesives that do away with the "pop off" problem. Walmart carries a double sided tape in a disposable container called Easy-Stick by Manco -- I use the permanent variety. It comes in a four pack for under $9. It is applied in the same manner as mono-adhesive but the dispenser actually works and so does the tape.
My other favorite is carpet tape that I get at the dollar store (I get the really cheap kind that does not have the nylon fiber grid....that kind shows behind some light weight papers.) Carpet tape will hold ANYTHING to your card front....once it touches the paper it is there for perpetuity . If you make a mistake in positioning it can be lifted with Scrapper Solution sticker remover, but other than that once it's on it's not coming off!
I also like the 3-D glue dots when you need dimension - they have incredible adhesion.
Good luck in your seach for an adhesive you have confidence in and like to use; what one person likes the next may not care for