In general, lifetime appointments to the Federal bench are constitutionally important because they create a branch of the federal government, responsible for interpreting the law, that is independent of both the popular will (which is not always synonymous with what is constitutional) and the presidential and congressional politics associated with that popular will. It divorces emotion, or at least makes a serious attempt to do so, from the scholarly application and interpretation of the highest law in the land. This independent judiciary is a key focus of the Constitution's design, as well as our democracy's.
Specifically, Perry's proposal calls for ending lifetime appointments so that what he terms "activist judges", those he feels legislate from the bench rather than simply interpret existing law, can be removed by the President or Congress. To me this is dangerous on a few levels. Besides messing with the intentional framework of the Founding Fathers I mentioned earlier, it also begs the question: who gets to decide what an activist judge is? The partisan politics which already poisons so much of what Washington DC tries to do on a daily basis would then also infect the judicial system, as each sitting President or Congressional majority could essentially fire judges that did not interpret the law in their particular political preference. This alone means that judicial independence is lost, and the law automatically becomes less based on what the Constitution says and more based on what will keep judges their jobs.