A paper by Andrew Enterline and J. Michael Greig looks at the history of imposed democracies and the implications for Iraq and Afghanistan. I don’t think it necessarily helps to look only at that narrow subset of new democracies; I think the risk factors are similar for indigenous ones like the first French Republic. In any case, as Steve Muhlberger points out, Enterline and Greig’s criteria seem a bit daft: Canada and New Zealand imposed democracies? I don’t think so.
The paper looks at Polity IIId rankings as a tool to track the states. Eyeballing those ratings, some factors seem plausible to me.
How close to liberal democracy were previous regimes over the preceding hundred years, including not just elections, but an independent judiciary, rule of law, strong property rights, etc.? If the previous regime was colonial rule, how democratic was the ruling state, and how much local autonomy did the colony have? Much of the Philippines’ colonial history was under relatively illiberal Spanish control, while India got over a century of British rule. I think that mattered.
How much of the local economy is based on the extraction of resources like gold or oil? If it is, a predatory government can have a pleasant lifestyle while not paying a lot of attention to the general welfare of the citizens.
Finally, does the country have a meritocratic civil service, and is that institution well established? I don’t think this factor is generally given the importance it deserves. When civil service jobs are distributed by competitive written examination, on a model that goes back to Imperial China, they cease to be spoils to be fought over, and the incumbents have a vested interest in keeping it that way. (The ability of the exams to measure anything more than the candidates' fitness to write about, say, classical poetry seems to be largely secondary.) And a meritocratic civil service can exist regardless of whether or not the current regime is democratic.
A meritocratic civil service does seem to be a common factor in many of the new democracies that survived the transition from autocracy or colonial rule: countries as otherwise disparate as Germany, Japan, India, Malaysia, South Korea, Taiwan and Turkey.