Presidents are prohibited from running for a third term of office because

There are many valid reasons for this, but a need for and preventing corruption/dictatorship seem the best reason for me. It's a lot of power for one person, and in 8 years, a lot of good (but also a lot of damage) can be done.  8 years is enough for a good president to leave his mark on our country.  Going beyond that point, especially with lifetime appointments like Article III judges, potentially lets a president perpetuate his power for a generation