Does some degree of stubbornness help for a researcher?
Although I understand what you are getting at, I would like to say that stubbornness is perhaps not a good trait for a scientist. My dictionary provides the following: Stubborn: Having or showing dogged determination not to change one's attitude or position on something, esp. in spite of good arguments or reasons.

Clearly a scientist needs doggedness and stamina to endure long and hard experiments, field work, often monotonous work on data and theory, as well as other issues met in the workplace. To be able to change footing in light of new evidence is, however, an important trait. So being stubborn, in the sense of the definition, would be very counter productive in our effort to have science progress. Persistence and perseverance are perhaps synonyms that better reflect the traits you aim for.

So, yes it is important to be able to endure. Being a scientist is usually based on a deep appreciation for the subject and the research, which is why it is possible to endure the pressures that exist. It is a bit like being a top athlete, very few will excel without a deep love for what they do. As soon as you lose the drive it is difficult to continue because of the demands. Maintaining the drive is therefore a very important aspect of academia and the workplace in which you act.