Peel and Stick Weatherstripping
I don’t typically like peel and stick weatherstripping, but it does have its place. Generally, I find it to be a very temporary type of weatherization, but if you apply it to an area that doesn’t see a lot of movement, it should do well there.
Areas that don’t see a lot of use would be the attic hatch. Doors on the other hand, get lots of use daily and will fail sooner.
It seems that temperature extremes will cause many peel & stick surfaces to fail and then your weatherstripping falls down. Some tips to get the adhesive to stick longer are to apply the weatherstripping when the temperature is not extreme (between 40-90 degrees). Make sure the surface is clean, dry and grease-free.
Start at one corner, and peel the tape from the back of the weatherstrip. Firmly press the sticky side onto the surface. Peel the tape and continue applying the weatherstrip until the perimeter of whatever you are sealing is covered.
I would use the peel & stick as a last resort though. If your door or window has a groove or kerf for a specific style of weather stripping, I would certainly use that first. It tends to last a lot longer.