The Christian doesn't hold the burden of proof to answer every objection raised by a critic. If the critic asserts something without proof or with poor proof, you simply shift the burden back on them.
The feature article this week is an example of that - the difference between refuting and rebutting. A refutation answers the objection and the argument supporting it. Rebutting a claim shows why it doesn't go through and puts the ball back into the critic's court. Greg illustrates this in answering a claim that purports to disprove the Biblical flood. You can read it here. He simply points out why the assertion doesn't work, and sometimes it's as simple as that.
Don't take the obligation to answer every objection. Stop and consider whether it actually proves something. If it does, then do your best to answer it. If not, then let the critic make his case before you try to answer it.