Update: Escape is working with me, and a local Dometic service center, to fix the furnace. It is still unreliable.
Longer story...
On March 17, after the camper was brought back home, I tested the battery, battery connections, and furnace function. The battery measured 14.1v. The battery connections were tight. The furnace would not stay lit for more than 20 seconds whether on battery or 'shore power'.
I contacted Escape Trailer customer support, and they pointed me to contact Dometic since it was a warranty issue with an appliance. Dometic stated the furnace would need to be diagnosed by a local Dometic service center.
I took the camper to a local service center on March 22. They tested the furnace on March 22 and March 23, but they were unable to replicate the problem. They stated they could not contact Dometic about a warranty issue if they could not replicate the problem.
I spent a couple days communicating with Escape and Dometic. Escape restated that warranty issues with appliance had to be addressed by the appliance manufacturer. Dometic adamantly stated that the 'coach' manufacturer was responsible for covering new appliances.
Dometic even suggested the furnace had been installed improperly. There was no evidence from the service center that the furnace was installed improperly. So, I had a faulty, unreliable, 2-month old furnace that nobody was willing to help diagnose or fix.
Escape has stepped up and offered to work with a local Dometic service center to repair the furnace.
I will update this thread after the schedule service appointment in early May.
Sam