I've gotta agree w/ the 'politics' aspect of teams leaving..
There's also burnout. All the funding in the world can't keep people who need to spend time w/ their families and concentrate more on work from doing that. And it's just an overall exhaustion on people after a while.
So life lasts as long as the people can as well- if you have the great benefit of constantly gaining new people to take top roles in your team, you could literally last forever.
I'm currently on my second "10-year team"... I can see the politics starting to slow down T126 a bit.. but in many ways the burnout of the many wonderful engineers and supporters who have been with that team since their very first National Champion robot until today.
But in great contrast, my current team: 190. There is a great thriving and strength among the team because the main source of 'mentorship' comes from college students who are constantly flowing in and out of the program and in and out of the top time-consuming and exhausting roles. As well, the high school kids are only around for 1 or 2 years, so the freshness of the team keeps burnout from having the chance to occur and allows the team to keep going strong.
So my thoughts: it takes strong, un-politically motivated minds to keep teams running.. which means they are often new minds in the forefront every couple years. There will also be a way (like guys like the Rambots prove) to find the money and stuff.. you just have to have the desire.
Kinda like the reason the folks in Kokomo gave the "Team Spirit Award" to us at the IRI even though we only had 4 team members there.. it's 'embodiment of the FIRST spirit and a determination to spread the word of FIRST'.... when that exists.. teams will never die down.
Average team lifespan: as long as someone remembers the impact they had on their lives
corniness ended.