If I am not wrong, the duty of a Christian is simply to deliver the message to them.
I don't remember anything about any obligation to contend with them continually - if I'm not wrong, Jesus himself simply told his disciples when encountering a city whose people would not want to hear them to shake the dust off their feet and leave in peace(See Matthew 10)
It seems to be just personal choice if you want to continue contending with them.
Keep in mind, that Christians should not assemble together in friendly terms to those who claim to be Christian but are actually fakes.