This isn't possible as scripts have no access to the tracker controls.
I've never personally found a problem with tracks getting slower over time, but I imagine this is mostly down to all the frame caching AE's doing when loading in each frame as it does the track. I can't think of a good reason why stopping/starting would speed things up much either.
When you stop/start a track it is then looking for the search feature as it was on that last frame, so stop/starting can certainly help at times. But then that depends slightly on how you have your search options set already. For example, if set to "Continue Tracking" it will always search for the feature as it was on the frame you started on making it more likely to need to stop/start the track, whereas when set to "Adapt Feature" it will update the search feature if it changes substantially over time.