Renewal of postdoctoral appointment
My feeling is that unless there are funding issues, there would be some resistance to firing a postdoc unless there were real problems: the startup cost/time for a new postdoc can be high. 

Having posted ads like these myself before, I can say that one non-funding-based reason to mention a 1-2 year postdoc is to allow for a hedge in case the hired person turns out to be really bad. In that case, you have the option of doing a first-year review and dismissing the person (i.e the default bit is set to NO and some activation energy is required to make it a YES)

In the reverse case of a two-year postdoc, the default bit is now YES and significant activation energy is required to make it a NO. If not done right, this could even lead to charges of unfair dismissal and so on. 

So since there's a glut of postdocs and a short supply of positions, the "buyers" have some power to shape the position to suit their needs.