"Secondly, how is cleaning it going to fix the fact that the power just needs to be reset on the player for the sound to come out? if the sound gets there flawlessly and then fails after a while, then why would the connectors being clean help?"

Because I heard that other people were having problems with dirty docking connectors.

"but what do you mean by continuity from plug to pinout?"

Its just checking the connection to see if it is complete. Using a electrical tester to test the physical connection between the L speaker rca cable and the L speaker pin on the docking connector. It obviously works part of the time anyway, since it works for 5 min at a time. I'm not an electrician, but I do have to work on electronics all the time at work. Loose connections can cause strange things to happen.

Sean