Amalgam fillings, also called "silver" fillings, sometimes, but not always, need to be replaced. If the filling is quite old, the edges may break down and allow fluids and bacteria to enter, which can lead to a cavity developing underneath. This is true for both silver and white fillings.
There are often stress fractures around silver fillings, and this can be another reason to remove the silver filling. Silver fillings can expand with temperature changes and can lead to tooth fracture. For more information about stress fractures caused by silver fillings, check out this article on PubMed.
If the silver filling is well intact and there is no recurrent cavity or enamel fractures, then it is okay to leave it alone.