New outdoor package unit furnace sometimes fails to ignite

I live in the southern US in an old house with an outdoor gas/electric package unit heating and cooling the first floor. A few months ago I woke up one morning to find that the heat downstairs had not turned on overnight even though my thermostat said it had been running for 3 hours straight.

The problem seemed to be that the furnace outside was starting up, failing to ignite (Standing next to the unit I could hear the sound of the igniter for a few seconds and smell the gas but then it would stop and the exhaust would still be running cold), and then just cycling on and off. Later in the day sometimes it would start and sometimes it wouldn't.

I called an HVAC company who came and told me the heating elements had corroded and the unit was unsafe. They turned off the gas and I got the unit replaced, but a few days later I had the same problem with the new unit. I called the HVAC company again and the guy came out and replaced a section of low-voltage wire that had frayed near the unit, but the next day the heat failed to come on again. I called again and the guy came out and said it must be that my Nest thermostat was malfunctioning, so they installed a new Honeywell thermostat. A few days later, same deal, no heat in the morning. I took it upon myself to run an entirely fresh low-voltage wire all the way from the thermostat, through the crawlspace to the junction box outside where the HVAC guy had replaced the final run into the unit, but this morning I still have the same problem. So, with fresh wiring, a brand new thermostat and package unit, what else could be causing the ignition failure only some of the time?