I like my students to work on a few pieces at a time. I give them (or they choose) a 'challenge' piece, i.e. something that is quite difficult for them and will need to study for a while (... 3 months to me is still a l o n g time to be working on one piece, it tells me that the piece is still a little 'beyond' them). I have an informal recital every term in my studio (and a term is about 10 weeks), and a formal recital (open to the public) at the end of the year. My students prepare a 'challenge' piece for every recital.
They also have other assignments that aren't as difficult. Sometimes I give them two or three weeks to complete it (the idea is just to set a goal to work towards - I don't chop their heads off if they don't reach their goal), others I expect at performance standard in one week (these are very achievable for them).
I like the idea of students coming across the different skills required with contrasting pieces regularly. Small gradul stepping stones they can manage until they come to a piece such as "Fur Elise" and can manage it within the month or so, and then move on to something else.
I do concentrate quite a bit on similar standard pieces before we go up a notch.
I really liked Steve's comment in another thread where he said something about if you can't recognise the difficulty of a piece, you aren't ready for it.
I guess I like to get my students 'ready' before they tackle anything that will take them longer than three months. I don't have any of my students working on just one piece for three months.
On average I like to set a goal for students to achieve between 5 - 8 pieces every term. The pieces will be at varying standards though - one or two very difficult, perhaps one ridiculously easy, a few more about a similar standard, etc.
I do this because I believe if practising intensities are variable, it is easier to keep interest, feel you are achieving frequently, and maintain motivation.
I also love so much of the music out there that I want my students to experience it as much as possible. They have their whole lives ahead of them to tackle whatever difficult piece they like.