Why is some mid century modern furniture missing labels?  

Your chairs are not danish. I don't believe they would even be considered danish style. Paper labels fall off, also people remove label after they purchase furniture.There are couple ways you can tell old furniture from new. Aged wood looks very different then new wood it also smells diferent. Old finishes look old and new finishes look new.

If someone were to make the same chair today it probaly would sell for the same amount you paid for your chairs, or more. I don't think it would benefit anyone to make copies and try to sell those chairs as originals. Simply because they are not hugely desirable chairs.

Are they even the same chair as in the advertisement. It looks too low res to be able to say the chair is anything more than similar.

You need to figure out if the chair is actually the same design as in the photo. You need to figure out how Drexel marked these chairs. You need to figure out how reliably Drexel marked its furniture.

And if they did have labels at one time, why aren't they saved and put back on when the furniture is refurbished?

I've reupholstered a lot of furniture made in the 50s and 60s, much of it already reupholstered in the past at least once. Upholstery fabric lasts 15-20 years, so if a chair was made in 1955, it would likely be reupholstered in the early 70s. People also reupholster because they want a new look (to go with a new sofa, or new carpet, or new whatever---there are lots of reasons for change.

Back in the 70s, mid-century modern style wasn't the hot new thing, it was just...older furniture. I doubt that there were many people who thought it was important to save paper or fabric labels and stick them back on after refinishing or reupholstering. I always save and reattach labels because now it matters, but most of the time the original label is long gone.

Also, on most upholstered American furniture, the labels were attached to the cushion or the deck fabric under the seat cushion, all of which would get tossed. It's just how things were done. A lot of Scandinavian furniture from the 50s and 60s was more about the frame than the upholstery, and they marked the frames either by incising or stamping the wood or by glueing labels to the wood. Rarely did the upholstery get tagged.

Drexel was pretty good about marking their tables and case goods with clear stencils. Larger upholstered pieces got an embroidered fabric label affixed to the deck and a "law label" tacked to the underside. Custom and contract pieces sometimes got a work-order tag under there, too. Loose-cushion chairs like the OP's often got nothing beyond the ubiquitous "law label".