I investigated this question because of its potential relevance to existential risk and the long-term future more generally. There are a limited number of books and scientific papers on the topic and the core questions are generally not regarded as resolved, but the people who seem most informed about the issue generally believe that space colonization will eventually be possible. I found no books or scientific papers arguing for in-principle infeasibility, and believe I would have found important ones if they existed. The blog posts and journalistic pieces arguing for the infeasibility of space colonization are largely unconvincing due to lack of depth and failure to engage with relevant counterarguments.
The potential obstacles to space colonization include: very large energy requirements, health and reproductive challenges from microgravity and cosmic radiation, short human lifespans in comparison with great distances for interstellar travel, maintaining a minimal level of genetic diversity, finding a hospitable target, substantial scale requirements for building another civilization, economic challenges due to large costs and delayed returns, and potential political resistance. Each of these obstacles has various proposed solutions and/or arguments that the problem is not insurmountable. Many of these obstacles would be easier to overcome given potential advances in AI, robotics, manufacturing, and propulsion technology.
Deeper investigation of this topic could address the feasibility of the relevant advances in AI, robotics, manufacturing, and propulsion technology. My intuition is that such investigation would lend further support to the conclusion that interstellar colonization will eventually be possible.
Note: This investigation relied significantly on interviews and Wikipedia articles because I’m unfamiliar with the area, there are not many very authoritative sources, and I was trying to review this question quickly.
An attempt from Nick Beckstead on almost this question:
Will we eventually be able to colonize other stars? Notes from a preliminary review (June 2014)