How do I handle a long gap on my résumé?

My résumé shows a gap from a layoff and some health issues. I am nervous about being filtered out. Did anyone get past it?

I was hired after a 6-month gap. The manager said the skills test mattered more than the dates.

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.