Originally posted by Tim the Enchanter
There is no term of office for the Muggle Prime Minister. He (or she, in the case of Thatcher) simply stays in power for as long as his party or party coalition retains a majority in Parliament. However, a PM could also lose his position by dying or being rendered invalid somehow, by resigning, or by being voted out of office by a vote of no confidence. Since there aren't any political parties in the wizarding world (that we're aware of), the Minister for Magic would probably stay in office until he dies, retires or resigns, or is voted out.