I'm reading an interview with Jean-Loup Puget, the principal investigator for the High Frequency Instrument on Planck, in the particle physics newsletter ÉLÉMENTAÍRE (you can find it here -- it's in French).

In it, he recounts how we almost missed a problem during testing which would have ruined the mission. Basically, on the last day of testing (there was about a month of testing before the launch), the instrument team found a helium leak that could have compromised the project. It only appeared on the last day of testing. If it had 'held out' just a day longer, we would have had no idea that it existed before the satellite was beyond reach and we would not have been able to repair it.

The basic problem was a faulty pressure regulator. There were still hiccups even after the problem was found. There aren't a lot of these kinds of regulators approved for space use, and the usual lead time needed to get one of them is eight months. An extra eight-month delay in the launch would have meant a lot of frustration for us, and a lot of money for the European Space Agency. But in the end they found replacements by "borrowing" similar regulators which had been approved for another satellite.