Really though, it doesn't matter what factory reconditioned means. What really matters is the warranty. Not all monitors (this applies to everything else) are created equal. Just because one monitor is running for x amount of years doesn't mean that the other one will do just the same. Now from the bigger picture, if you have like 1 person having a bad monitor out of 1000, that's a pretty damn good batch, and I wouldn't worry too much about the monitor going bad.
Things like monitors, I'd stick with ones that have at least a 3 year parts/labor warranty, whether it be new or reconditioned. What do you think TV/Monitor repair men do for a living???