If you take the path integral of a dissipative force from point A to point B along a certain path 1, and you take the same path integral from point A to point B along a different path 2, you will not get the same answer. In other words, the work it requires to move from point A to point B is path dependent for a dissipative force. As a result, it is impossible to define a unique work function that is independent of path, and so there is no way to define a unique potential at any point in space.
For a non-dissipative force, the path integral is independent of the path, and so in that case, you can define a unique work function and a unique potential at every point in space.
