Some churches who appoint elders do so for a term (3 years is typical from what I have seen). Other churches ordain elders for life. Is there a Biblical basis for ordaining elders for a term?
Some people in the Bible who had leadership roles held those roles for life. For example, the Old Testament kings and the New Testament apostles apparently held leadership roles for life. Others held temporary posts, like the Judges. I don't recall any place in the Bible where someone held an office for a fixed amount of time, as is common today. But as Flimzy says, nothing in the Bible says that any office must be for life or for a specific term. (Well, except "husband" and "wife", if you think of those as offices.) At least, I can't think of any.
In my tradition, which is Swedish pentecostal, the traditional view is that you are an elder for life. This used to be said with reference to Romans 11:29
...Gods [...] call are irrevocable (NIV). That is however not very good hermeneutic. That passage refers to the calling of the people of Israel. Maybe you could argue that this also refers to Gods call for every person that belong to him through the faith of Jesus Christ. But you can't say that this speaks about the calling for a certain service in the church.
I would'nt say that there are a good biblical basis to say that you are an elder for life time. But I would say, and that is an personal opinion, that the texts (specially in the pastoral letters) takes the service to be an elder very serious. And it wouldn't be true to the seriousness of this service to let it rotate for every three years or something.