One of the great negotiating tactics is to switch gears when things look dim. As a salesperson of over twenty years, I have become keenly aware of this particular practice. I'm sure I've encountered it many times. When a particular point of negotiation is "going south" gently set it aside and agree to come back to it later. Meanwhile move on to another area where your position is stronger.
Interestingly, I've had conversations like this with several agnostics as well. The moment a point seems hopeless, the subject will quickly change to a completely different area. I can recall one such conversation that I had with a business associate where we casually debated the theory of evolution versus creation by God. The moment I started revealing some of the facts about the fossil record evidence he quickly changed the subject to attacking the Bible as God's word. I made the mistake of chasing that argument and several others with suitable defenses. It would have been more productive to insist on sticking to the point.
Does the fossil record support evolution or not? When that question is answered we can move on. As it was we had a lot of debate and never reached any conclusions. Since that time I've learned the importance of staying on topic until truth is exposed. One final note on this topic should be taken about the importance of some arguments. Sometimes skeptics toss out assertions right and left, many of which are trivial. Try to get to the important points.