They are allowed to move. In fact, if you think about it for a minute you can see that Lorentz invariance requires that they be allowed to move because given a static brane I can always boost to a reference frame where the brane is moving. In order for this to be an equally good description of the physics we must allow branes to move.
As an aside, the same logic is often used when constructing solitons. We start by determining the solution for a static soliton because it is easier, but we know that it must be able to move in order for the Lorentz invariance to be respected.
In practice we tend to ignore the dynamics of D-branes because they are so massive, but in principle they can move and be accelerated.