How can one find a promising research project that doesn't just fall apart? I'm just starting my second year of a master's program and hoping to apply to PhD programs, but I still haven't even submitted a paper for publication. I've worked on 3 research projects over the past 3 years, all of which have fallen apart for different reasons. [EDIT: They fell apart not because they didn't validate my hypothesis or something, but in two cases, because of advisor drama and in one case because another student found a significant flaw.) How can I choose my next project in such a way that minimizes the chances that it'll also just fall apart? 

My experience with these abandoned projects has, I believe, taught me three things:  


Vet potential advisors more thoroughly, 
Don't waste time on a project you don't think is all that promising right from the get-go, and 
Get on a project with a team, not one that you'll work on individually.  


However, my experience has also shown me that: 


It's really impossible to know what an advisor is like until you've already crashed and burned with them. 
Good projects are hard, if not impossible, to come by. At the time that I worked on the projects that fell apart, they were basically my best options. 
Having to find a team to work with puts you at the mercy of whether people a) have something you're even able to do, b) are actually good to work with, and c) want to work with you (unless, I guess, you're just assigned to the team by your advisor). I've already been shot down by one potential research partner.  


Meanwhile, I know of an undergrad who worked on a project for one quarter and now has a publication at a major conference. Do I just have to face the fact that I'm not cut out for this research stuff? I'm starting to get the impression that I'm just a "quitter," but I feel that every time I've quit, I've done so for completely valid reasons, not just because the "going got tough."  

Is there something I'm not thinking of or doing in order to find a good project and take it all the way through to completion?
The fact that your projects failed should not be a bar to your continuing on to a Ph.D. program. The reality of research is that most research fails! Remember that Edison tried over a thousand combinations before finding one to work for his light bulb. Nobody is 100 percent successful in research and projects end up falling short of expectations or failing altogether a substantial percentage of the time. It's how you persevere through the failures that distinguishes a successful researcher from an unsuccessful one.

Moreover, projects working or not working can be a matter of luck, and sometimes it can take an extended period of time to make a breakthrough. During my Ph.D. project, I had basically nothing but failed approaches to show for two and a half years (!) before I had my "Eureka!" moment. I wrote six papers in the remaining three and a half years after that. 

So I wouldn't worry about finding a "good" project: ideas that seem sound on first blush can fall through, and a "high-risk, high-reward" type project can lead to big breakthroughs in the long run. Focus on doing something that interests you, so that you can keep going when you run into rough patches (and they will come).