When Christ commanded that we should forgive one another 'seventy times seven', it was in response to a scenario in which one disciple were to forgive another disciple. In essence, fellow Believers are to offer unrestricted and unlimited forgiveness to one another.
Christ did not, however, indicate how many times we are to forgive NON-Believers. Earlier in the lesson, he said to 'turn the other cheek.' The human body has a very finite and limited number of cheeks to be turned.
Welcome to the site, Bob.
But I have to disagree with you very strongly here. Bruce is right to point out this is exactly the kind of thinking that drives a wedge between Christians and those they interact with. It's a sort of contradiction because ideally fellow Christians would require forgiveness less often than those who don't follow Christ's teachings.
The verse you referenced is Matthew 18:22, but if you go on and read the rest of the chapter, Jesus sets up an analogy of a master who forgave the debt of a servant, but then the servant went out and refused to forgive the debt of another man who asked it of him, and so the master became angry and forced the servant to repay him after all.
Nowhere in that parable does it suggest that the rules are different for some than for others.
"He who takes offense when no offense is intended is a fool, and he who takes offense when offense is intended is a greater fool."
"Don't take refuge in the false security of consensus."