The problem with the Federal Courts is similar to the problem with Congress. If you find the right person, they should serve as long as possible.
If you're not finding the right people, adding term limits isn't going to help.
After the civil war, all of the states appointed judges the same way the federal government does. The executive would appoint a judge, the legislature would confirm or deny the appointment. It's an easily corrupted system. Presidents routinely appoint people with no experience to be federal judges for life, and they try to find true ideologues for the highest positions.
The progressive movement of the late 1800s/ early 1900s saw this was a problem, and they successfully changed almost every state constitution to make state judges more accountable to the people and make sure they actually had legal experience. Today, only New Jersey still appoints judges the old way.
If that first progressive movement had succeeded in amending the US constitution along the same lines, we'd be in much less of a pickle.

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