Essentially, this was the matter of one's style in the context of inevitable changes in stylistic fashion. An illustrator with a widely recognized style -- one whose work can be identified at a glance -- can rake in plenty of income while that kind of style remains fashionable. But when the fashion changes from, say, painterly brushwork in oils (1915-1927 or so) to thin linework and watercolor (1928-1935 or so), one's happy career could easily crash.
Other than dropping out of illustration to become an art director, taking up portrait painting, teaching and other non-illustration possibilities, the successful illustrator has two main strategic career alternatives. One is to continue his basic style, perhaps with a few minor adjustments. Norman Rockwell and J.C. Leyendecker did this, though Leyendecker's popularity eventually faded whereas Rockwell's did not. I suspect that this holding-the-fort strategy is rarely successful.
The alternative strategy is to try going with the fashion flow. That is, changing one's style and (if necessary) one's preferred medium. This can be very difficult for well-known illustrators because, all of a sudden, they aren't producing what made them popular in the first place. One successful example of this style shift is Mead Schaeffer, whose 1940s work is noticeably different from what he was doing in the 1920s and 1930s. Dean Cornwell shifted his style enough to stay competitive, but John La Gatta's career began to fade as he tried to adjust to the times.
Changing illustration style fashions often worked to the advantage of artists who were fairly successful, but not as famous as the ones just mentioned. The reason is, by not being famous, their initial style hadn't become a strong trademark. So as long as they were competent and could easily practice the new fashion, their careers could continue chugging along.
The present post deals with a top-level illustrator who never had a strongly identifiable style, and therefore easily went along with the changing scene, happily earning a nice income.
Floyd MacMillan Davis (1896-1966), known simply as Floyd Davis, thrived from the mid-1920s into the 1950s, though he dialed back by the latter decade. Background information can be found here and here as well as elsewhere on the Internet and in several books dealing with American illustrators.
Briefly, Davis never had serious formal training. He had a knack for illustration, and that was enough in his case. It seems he seldom used models -- unusual for other top-earning illustrators. And his work could include caricature-like distortions and small, humorous details that did not interfere with his main theme. As for how he approached his work, here is the text of a 1942 interview of Davis by Ernest W. Watson.
Below are examples of Davis' work. I have to admit that I find it surprising that he was so well-known and successful, given the visual variety of his output. All that I can offer is the thought that Floyd Davis was the anti- Normal Rockwell.
here and here. The style Davis used here is quite different from the other shown here.