How can I repair a delaminating outside door?

Easier done with the door removed.. Remove any loose veneer. Cut with a razor knife. Do not pull or it will come off in strips. Use auto body filler to fill the the spots with a putty knife. Let that cure and harden. Sand it smooth with the door surface. Prime and paint.

What about covering it with a kick plate?

Here is a step by step source

http://littlegreennotebook.blogspot.com/2014/10/diy-on-fixing-up-chipped-veneer.html?m=1

Bondo actually makes wood filler if your door is wooden. If not use the regular auto body filler, but you have to be fast when mixing and applying. That stuff hardens quickly. I agree with William. Sand, smooth and paint. I think covering with a kick plate is just covering up the problem, not the solution.

I believe there is a metal sill that can on the bottom of your door, and just needs to be screwed into the door. There fore, this will look real nice, and no more problems. These are available at hardware stores. Best wishes, J.

I'm not sure of all the big box stores but many full service lumber yards in my neighborhood carry 1/8" thick door skins but you would have to apply a marine epoxy to it our you would just be redoing this process.