Disney's movie Snow White and the Seven Dwarves was a groundbreaker in its original 1937 release -- while not technically the first full-length animated movie (that honor goes to the Argentinian Quirino Cristiani with El Apostol from 1917) it can still be termed the first "traditionally" animated one.

It was also a groundbreaker on its re-release, in 1944, making bucketfuls of money despite being a reissue, and later went on to get further re-releases in 1952, 1958, 1967, 1975, 1983, 1987 and 1993.

Reissues were nothing new, going back nearly to the start of films, but they were generally done at low prices compared to new films. What happened with the 1940s was a shortage such that old films starting getting reissued with prices like they were new films, and the reissue market in general blew up. Even with this, theaters had trouble keeping up film schedules, and started to extend their film showing periods (roughly a week). As Variety from October 15, 1941 notes it partly stems from an "effort to get along on less film".

This continued after WW2: 1947 had 53 reissues, 1948 had 105, 1949 had 136. (Variety from 1947: "One in Every Five Pix Showing in NY a Reissue".) This wasn't just pumping for money; there was a general decline amongst film profits (which became even larger through the 50s and the boom in television popularity) and reissues were a way to help stay afloat.

However, there's still a major issue with your premise, in that it sounds like you're hoping for a repeat in the same theater soon after missing a showing. Snow White is one of the most re-issued movies I can think of, and you'll notice the spans between releases are rather longer than you're probably hoping for.

It might be possible to catch a showing in a different theater. Second-run theaters were definitely a thing in the 1950s and long before, all the way again nearly to the start of cinema. Theaters were designated first-run, second-run, or even third-run, and first-run theaters would get a "run" followed by a "clearance" where a film would not show at all in a particular zone; then the "second-run" theaters could get their run, and so on, with second-run being cheaper than first-run and so forth. You wouldn't necessarily be able to find a second or third-run showing anywhere nearby, though.

The other option is television, although that could be hit-or-miss. If you're a fan with horror movies of the 1930s and 1940s, you're set on television in 1950s with the popularity of the "horror host". In general, there were issues with contract negotiations, and entirely different issues with the appearance of looking like a B-movie factory. Paramount wanted to license movies but went through a complicated series of shell companies to appear that "Paramount brand" films were good enough only for theaters, while simultaneously dropping their lesser movies into television rotation. It wasn't until the mid-1950s that there were regular major studio contracts and not until the 1960s that there was something approaching a pipeline, although it'd be rather hopeful to try to catch a particular movie -- it wasn't required or regularized to have a particular movie show on television.

There could theoretically have been yet another option, that of paid television for seeing theatrical showings. Paramount (which funded the start of the TV company DuMont) was very interested in this quite early; in 1942 they bought a company named Scophony exploring this very idea, and continued working on the idea through DuMont and later using a technology called Telemeter. There were some major regulatory obstacles (with some suspicion of trying to worm around the breaking up of the "vertical monopoly" which used to link studios directly to movie theaters). Regulatory rules from the FCC on pay television were only established in 1968 and Paramount's efforts more or less fell apart being dragged through monetary and legal debates.

In general summary: yes, for the most part, if you missed all the runs of a particular movie, except in special circumstances, through the 1950s and 1960s you were out of luck.

(You mentioned the 1970s, but you could get yourself a Avco Cartrivision -- first out in 1972 -- and rent actual films. The rental-only films didn't let you watch twice and could only be rewound by a dealer. VCR really started getting big around 1975. So that's more or less out of the range in your question.)

ADD: A couple other options, consolidating some of my follow-up comments:

1.) The first revival theaters were in 1938 NYC, and some of the "canonical films" were shown repeatedly enough that you could catch, say, The Rules of the Game without much difficulty. So your theoretical movie-watcher might be in luck if their missed film ended up in the art canon.

2.) Super 8 consumer market for buying films started roughly 1970 and was reasonably affordable. 16mm was not so much, although it was possible. (The good news if you managed to get one it was possible to rent a film just like a regular theater, although they tended to be from an older scattershot collection. This catalog is pretty representative. The bad news is it was still expensive. Getting a rental -- remember, not buying -- the 1961 film Greyfriars Bobby in the 1967 catalog is listed as $24.50; after inflation, that's ~$206 in 2022 money.) There were quite a few regular 8mm projectors through the 50s and 60s but their catalogs involved shorts.

...

You can watch the 1944 trailer for Snow White and the Seven Dwarves here at Youtube.

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Gomery, D. (1992). Shared Pleasures: A History of Movie Presentation in the United States. University of Wisconsin Press.

Hannan, B. (2016). Coming Back to a Theater Near You: A History of Hollywood Reissues, 1914-2014. McFarland.

Hoyt, E. (2014). Hollywood Vault: Film Libraries Before Home Video. United States: University of California Press.

Ward, R. L. (2006). A History of the Hal Roach Studios. United States: Southern Illinois University Press.

White, T. R. (1988). Life after Divorce: The Corporate Strategy of Paramount Pictures Corporation in the 1950s. Film History, 2(2), 99–119. http://www.jstor.org/stable/3815029

Williams, P. (1994). The Evolution of the Television Rerun, Journal of Popular Film and Television, 21:4, 162-175.