I understand your dilemma, being new to the patch and getting conflicting information. However, there's the literature, and there's real life. Reapplying a patch that has come off does not make it dispense any faster - if anything, it will go slower because the skin port that forms under the patch is what has been compromised. You are in more danger of overdosing by being out in the heat and sweating while wearing the patch, rather than taping on one that has fallen off.
I can't count the number of times I've had a patch come off and had to re-tape it. It even happened with the very first one I applied when I took a shower that evening. I never experienced any ill effects from doing so. Now, had I played by the rules and simply thrown them away and applied a new one, it would have been a huge problem with not only my doctor, but my insurance company. I can tell you that truthfully because I DID play by the rules the first few months and got accused of using the patches improperly. My insurance company balked at paying for more patches than were prescribed for a one month supply and the doctor had to practically sign in blood to get it covered.
Obviously, the best thing to do is make sure they never come off - not always an easy thing. Using tegaderm as a cover has worked very well for me and I now rarely have a patch fall off.
Hope things work out OK for you with the patch. It can take some adjustment, but at least for me, it works very well.
Living in the Republic of Texas minus a gallbladder, a couple of cervical discs, appendix, uterus, and 18" of colon; but living with my wonderful husband, 2 dogs, 1 cockatiel, and 2 gold fish.