Ask HN: Hourly freelancers, what do you do when you can't figure something out?

I'm stuck on a particularly irritating show-stopping bug (microchip's ADC functionality just giving 0 no matter what voltage is applied) and haven't been able to find a solution in days. I feel guilty continuing to charge for the many, many hours of investigation without producing anything....it's just making me feel incompetent and thieving.

Has this ever happened to you, and if so how did you handle it? Do you keep charging, or work for free, or just tell them "sorry, you have to hire someone else to complete this, I just don't know why this is happening" ?