Even as a team that has participted in FIRST for 3 years now we still have major difficulty entering the competition each year. The problems really fall into two categories: Money and Faculty.
Money has always been an issue for us. In terms of school funding, we get next to nothing. Our school board won't sponsor us, and our school is only willing to give us $50. So we always have to find a lot of sponsors each year. Luckily this year we found a great sponsor/mentor who helped us greatly.
Faculty is also starting to become an issue. Our team only has one teacher sponsor and it is not reasonable for us to ask him to supervise us every meeting. He's a very busy person. We found another teacher sponsor to help us this year and that has helped, but faculty is still a big issue. Our mentor offered his shop to us, but that brought up another problem and that's transportation. Most of our meetings are held after school and bringing 20 or so students to his shop is difficult, especially in Canadian winters.
School rules are also a problem, but luckily our principle is fully behind the robotics program and even found us a very generous sponsor.
However, I think for most teams, these are the common barriers to entry.