I think that the law is timeless, but people that interpret the law are not. It may not be disclosed or even frowned upon and flat out illegal, but some on the panel are politically bias and support one party over the other, no matter what the law says. Being a career Justice is not good for America. Times change and sometimes people too. A fresh face every 10 years is good for everyone no matter what party or view you support.
Yes, term limits sound like a good idea. Re-election should not be an option, however, as that can lead to bending decisions towards the biggest donor or largest ruling party. We all know that there are liberal, conservative, and moderate justices in the Supreme Court. Why not institutionalize this? Enact the 3-3-3 principle: 3 liberal justices, 3 moderate justices, and 3 conservative justices. Then, justices can be appointed or elected and not sway the court too much.
The main reason why justices were given lifelong appointments in the first place was to reduce bias in their rulings. If their terms were limited to a number of years, then justices might develop a partisan slant when ruling on cases to increase their chances of re-election. This would hamper their ability to make fair and impartial decisions, and the Court would then become just as partisan as Congress.