There are a number of possibilities for your great-aunt, but we'll probably never know which is it unless you find her extensive set of diaries hidden somewhere.

A pretty big reason for a woman of this period to remain unmarried would be if she were not interested in men. Despite the taboo nature of all orientations but heterosexuality in the nineteenth and early twentieth centuries, non-straight people did exist! It can be hard to find evidence of sometimes because of a concept which grew up in the late eighteenth century and was in full flower through the nineteenth, known as "romantic friendship": a relationship that blurred the lines between deep platonic friendship and romantic love. Such a relationship was supposed to be the ideal, matching the deep passion of a heterosexual romance with the purity and understanding of a friendship between two women. It was also a great cover for two women having an actual romantic relationship. When you read correspondence between the members of what's sometimes called a "Boston marriage" (two middle- or upper-class women sharing a home in the nineteenth century), it is rarely explicit - even noted lesbian diarist Anne Lister put anything remotely spicy into code - and could plausibly be describing an intense and very intimate friendship. People by and large ignored the possibility of physical relations between women, portraying romantic expression between two women as acceptable practice for heterosexual marriage, in comparison to the concern they showed over male sexual desire for other men, unless it was linked to a crime or the women's rights movement (which, to be fair, did include quite a few women who were attracted to other women, like Sophonisba Breckenridge). Unmarried, virgin women were assumed to have no sex drive, so it was hard for society at large to think they could get up to anything. As lesbianism became more accepted as a real thing (and pathologized) in the twentieth century, the concept of the pure romantic friendship was firmly put in the past and assumed to be impossible.

Another reason was for a woman to have a career. Now, it wasn't impossible for a married woman to work - but it could be a significant barrier. First off, until the second half of the twentieth century, it was assumed that the first priority of a woman who was married should and would be her husband; while a poor couple might both need to work, the aspirational ideal was for the husband to provide enough money for his wife to concentrate on the labor of making his home comfortable through housekeeping and cooking. Married women who chose to work outside the home when they weren't forced to by financial necessity were somewhat uncommon, and the vast majority of husbands would have been at least uncomfortable with the idea, if not actively against it. And without access to reliable birth control, a working married woman in the early twentieth century would have likely ended up pregnant, which would certainly have ended her career. The only way for a middle-class woman to keep her job in her own hands was to stay safely single. (Did she keep working after moving to Denver?)

But, as you've mentioned, her health may have also been part of it. In the 1920s, tuberculosis was still not fully understood; they finally understood that it was a contagious rather than hereditary disease, at least, and there were better methods of early detection, but there was no cure. The best treatment was believed to be a stay in a sanatorium in the country, preferably in the mountains or in a hot and dry climate, although surgery could be performed on the lungs for very advanced cases. It was popularly believed that people with active tuberculosis would transmit the disease to a spouse, and that pregnancy could be extremely dangerous for tubercular women, although the National Tuberculosis Association strenuously objected - in 1919, the New Jersey Court of Chancery found that concealing tuberculosis from a prospective spouse could be grounds for annulment on the basis that it was a dangerous fraud. So it's entirely plausible in your great-aunt's specific situation that she felt that her condition meant that she could never marry, and that the men in her life automatically viewed her as a non-prospect.