A long run, a short run. We say of a drame, “It had a long run,” meaning it attracted the people to the house, and was represented over and over again for many nights. The allusion is to a runner who continues his race for a long way. The drama ran on night after night without change.
In the long run. In the final result. This allusion is to race-running: one may get the start for a time, but in the long run, or entire race, the result may be different. The hare got the start, but in the long run the patient perseverance of the tortoise won the race.
To go with a run. A seaman's phrase. A rope goes with a run when it is let go entirely, instead of being slackened gradually.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894