HVAC furnace igniter causing micro reset
I've worked with PICs for the last five years in industrial settings, and I've kept a list of the causes of unexpected resets. It's reasonable to think your problem is in hardware and not software (though software shouldn't be completely discounted as a possibility!). The closest thing I've seen to what you describe is noise on the !MCLR pin. I've seen chips reset both because !MCLR is pulled low, and because it's pulled above the positive rail, even in situations where !MCLR should be disabled by the configuration bits. Do you have any local cap on the !MCLR pin?

Failing that, you might also check to make sure your five volt rail is stable during this event. Do you have local cap on that, immediately at the chip?