Would You Replace A Stamp That Fell Off A Cover? How?

I store covers that have lost their stamps in poly cover sleeves with the stamp loose along with the cover. None of the ones I have currently is particularly valuable but I wish there was a good way to rejoin them without causing further damage. The only thing I can think of is to hinge the stamp in place.

Also I have a couple of covers that have stamps barely hanging on that I'm going to feel bad when they fall off. Is there a good way to prevent it?

What would you recommend?

Hinge the stamps that are off-cover back onto the covers in the same position where they were originally attached. That's acceptable. For those that are coming off cover, I don't know of a way to prevent them from coming off other than putting them in a protective covering/sleeve,handling them carefully and then if they do become detached, hinge them back onto the cover. That's my recommendation, perhaps someone else may have another solution for your questions.

Agree with Mr. Al 100%

A few years ago I actually had a Canadian cover from the 1940's where the stamp fell off, and and since mint examples of the stamp were so cheap, I found one with the selvedge attached. I moistened my finger, rubbed it around the gum on the selvage until it was mushy, then applied it to the loose stamp, and re-stuck it to the cover. It is still firmly attached - with original gum!