I have a Briant high efficiency furnace i.e
Air tight burner compartment, inducer motor
And exhaust and intake air from side of house
etc. I had similar problems with my gas furnace. I was able to solve the intermittent
Problem of the furnace not coming on every time the thermostat called for heat. I
Found that there was not enough oxygen entering into the burning chamber to light the
Last gas burner.. The furnace would try 4 times
To start and then it would shut down and have to be reset. Adding just a little room air to the
Burning chamber fixed the problem. Now my
Furnace comes on every time the thermostat
Calls for heat.

You didn't solve a problem, you treated a symptom. Sealed combustion units are intended to be sealed. If not properly addressed, something worse may develop.

Sorry I misspelled the brand name of the furnace. The Bryant furnace didn't work at all.
In fact the 2 previous owners called furnace repair people to resolve the problem with no
Luck followed by paying a lot of money for service calls. The previous owners had to heat
The house using the 2 gas fire places. They also turned on the electric dryer in an attempt
To keep warm in the winter. Using the dryer was dangerous as they restricted the hot air
Flow from the dryer.
The solution to the Bryant furnace problem did not endanger the occupants of the house.
The solution should have been made by the furnace repair people. The furnace has been
Running for 4 years without any failures and has run as an efficient unit. I think the problem occurred when the furnace was first designed and built. Increasing the fresh air
To the furnace (using a small fan in the fresh air in take) would probably been another solution that should have been incorporated by the manufacturer.

I agree with KC13. The furnace is probably installed wrong causing the problem.