How can one find a promising research project that doesn't just fall apart?
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).