Refusing to give up their seat? The people could just vote them out.
Sure, but I think that that doesn't do justice to some very real realities of the American political system. Not only do Senators like Cochran and often the party itself work to keep down potential intra-party challengers, but voters are often very incumbent-friendly for no real reason other than that person has been in office a long time. All of this makes it pretty difficult for
anyone, Republican, Democrat or Independent, to unseat them.
Personally, I would even settle for a limit as high as 3 terms. That is
18 years. Throw in a maximum age limit and we would really be getting somewhere. This isn't really a partisan idea. I know it's highly unlikely a Democrat would ever win a Mississippi Senate seat, except for maybe some freak Vitter-like scenario. This is about maintaining a government that has at least some unobstructed flow of new ideas on both sides of the aisle, and isn't bogged down by extremely old generational incumbents who simply refuse to let a new generation have a shot at molding the future of the country they, not the old people, will inherit.
So the Senate IS supposed to be full of the elder folks of the government.
Including people who are so old that they can't even think straight anymore? Elders doesn't necessarily mean those who have been there ~30 years and/or are literally dying in office. There is a difference.