I always have had a problem with the 3M blue tape. I no longer use it. Haven't for about 10 years now.
I know I have a thread on that somewhere on the forum.
I have good success with the green 1/16"
I know if you take a paint cleaner like DT330, it will get under the tape and gum it up. Once you remove it, it leaves the glue. I'm not for sure if this is the problem - probably not.
Also, if you leave the tape on for awhile, it may leave the adhesive.
Once you remove the tape though, you should be able to remove it with a subtle cleaner