I'm sure REU projects are abandoned a lot. It has to do mainly with the student's lack of direct contact with whoever they are working with over the summer. Also, it takes a while for the student to get up to speed with whatever project they pick up.
Here are some examples:
Two summers ago I spent a summer at an REU program working with a well-known theorist. It took me (as a 2nd year physics major) about 5 weeks to get up to speed, 3 weeks producing new results, and a week to write a report and prepare a presentation. I took a week off to attend a conference for an unrelated project. I took the project home, at the professor's request, and I started producing interesting results. I eventually lost contact with the researcher I was working with (he was out of the country for several months). This resulted in no publications.
This past summer I was invited to do research with a respectful theorist on a HEP-theory/differential geometry project. I already did research on the topic he was involved in (worked with one of his former students). It took me 4 weeks to reproduce results in two previously published papers of his and a week studying a very concentrated field of mathematics. I spent 3 weeks producing new results, a week at an undergraduate conference presenting results, and a week compiling all my notes for them. I got to attend a workshop and asked if I could continue the project as a senior thesis, I was denied because the professor was concerned about our lack of direct contact. Regardless, my name is going on the paper soon to be submitted for publication.
You can see that it doesn't always depend on the student's amount of work put into the project. I spent a summer and a semester rigorously working on the project that resulted in no publication, but spent only the summer and sparingly worked on some proofs throughout the semester for the project that resulted in a publication. It depends on the nature of the project itself (will it produce interesting results and are they achievable). Also, it depends on the connections established and previous experience in the field.