Having had to take a 6ish month break from igp I know full well about being relegated and am only now after a further 6 months being properly competitive again. This is because I found a league that was super active, with those competing in the league all being extremely respectful in regards to the racing side of things to each other, which makes for excellent competition. Albeit, a competition where some very active players are trailing around at the back, or in 10th/11th as well as those and the very sharp end of the race.
To permanently drop someone out of a league would not be the way to go as this punishes the players that dont yet have the experience they need in a new tier to be competitive.
I do have a couple of ideas for you though. Could you have a system that gives newly promoted teams a boost in development points so that their car is not permanently stuck at the back of the field, yet still giving them the choice on how they develop the car.
Could you also boost the experience gained from each race for a newly promoted team, this would also give these teams a better chance of staying in the higher tier once they've made it there.
As for capping tiers, could a scale of a level 5 cap for rookie, 10 for pro and 20/uncapped for elite work, or something along those lines.
You could also do the reverse of the boost for promoted teams for relegated teams so they for a season have lowered development and experience gains.
Not sure if that helps at all, but I feel that it's a suggestion that could help