I have the same problem as well. Although I have not been able to stick to it every time, I try to follow this method: If you are in an argument, keep the time in mind and change the subject as soon as you have not gained anything after e.g. 5 minutes. The gain could be new insights, entertainment, mental exercise, increase of social bonds/respect, money, self-respect, self actualization (e.g. convincing the influential person to implement your wish), etc. This sounds harsh, but time IS your most precious resource and using it without a benefit is like throwing money into a vending machine, which gives nothing in return. Better find another subject or conversation partner.

Deduct one minute every time the person switches talking points instead of responding to your argument. Punch him every time he mentions a study, but won't give you a source (e.g. instead of googling it together, he promises to 'send you a link later'). (Punching seems a bit excessive, but imagine a world in which everyone thought twice before quoting PIOOMA results! It could usher in a new age of enlightenment!)