How should I interpret a promising preprint that was never published in a peer-reviewed journal? There have been a couple of occasions in my research in which I've come across a preprint that is several years old and is very relevant to the work that I'm doing.

Often these preprints have very promising initial results. However, when looking at the CVs or Google Scholar pages of the authors on the preprint, I can't seem to find a version that ended up getting published in a peer-reviewed journal, even if the preprint is several years old already. Why would would a researcher abandon a manuscript that they obviously put a lot of time into?

Do researchers sometimes just abandon lines of inquiry because they get too busy?  Or, is this an indication that their promising initial results were not robust enough for peer-review, and I should be wary of attempting a similar study?
There might be any number of reasons. You might try to contact the author(s) to get more information. But... (not all with the same likelihood)

They might have left academia for various reasons and not bothered. Is the CV also old? 

They might have incorporated the key ideas into another paper with a very different title. You search is then fruitless.

They might have discovered errors. 

Reviewers might have considered the results trivial.

Their attempts to publish might have been rejected by journals for other reasons. 

They might have changed sub-fields. (This one less likely, I think.)

But you should be wary, at least, of following up on unpublished work and, at least, be sure that you can verify the claims independently.