Who really bears the burden of proof when debating? Traditionally, debates are either centered around a proposition or a question, and whoever argues in the affirmative bears the burden of proof. I would essentially agree with this principle because when it comes to debating the existence of god, usually it's the theist making the affirmative argument and I've consistently noticed an abject failure by most theists to demonstrate the truth of their theological beliefs.
However, although the person arguing the affirmative bears the initial burden of proof, any counter argument made should be backed up with evidence as the burden of proof lies on them to make the counter argument plausible. For example, if a debate is centered around creationism, and one makes the counter argument that evolution can explain away the need for a creator, then the evolutionist has the burden of proof to explain and show the evidence for evolution, or at least be able to produce evidence when prompted.
Also, the standard for the level of evidence required to back up a counter argument should be about equal to the level of evidence that was produced for the original argument. So if the evidence produced for the affirmative argument was circular, fatuous, or illogical, then the person making the counter argument need not stress over producing exceptional evidence. As Hitchens said, "What can be asserted without evidence, can be dismissed without evidence."
It's often hilarious dealing with the arguments theists will make in order "prove" the existence of one particular god. Some are halfway decent, and some are really, really bad. One of my favorite worst arguments for god is when a theist basically says, "It just seems so obvious to me that there's a God." I'm not sure if there's a name for this one, but it seems to be an argument from intuition or an argument from emotion akin to the "personal witness to the holy spirit" that theists like William Lane Craig think trumps all counter-evidence.
I don't see how it's "reasonable" to hold over all possible counter-evidence one's subjective experience of the divine, especially when it is known from neuroscience that the human brain can be fooled in a number of ways. This is why most theists who inoculate themselves with faith when all else fails, fail to be rational people, fail to own the burden of proof, and make themselves so difficult to deal with.