I assume this is a gas heater? and by the nature of your questions you are not familiar with it?
First advice: get someone to look at the unit ASAP. For some reason either the gas is not igniting properly when there is a call for heat or the flame sensor is not seeing the flame and shutting off the unit.
By removing the cover, you are resetting the safety system. Can you also get it to restart by turning off the breaker that feeds the furnace? If so, it is not a cover not making the door interlock switch (AKA rollout switch).
Since gas can go boom if things go badly or pipes can freeze and burst if the furnace totally fails and just stops working, PLEASE contact a service person to take a look at the problem.
No offence, but gas furnaces are no places for amateurs to play. -- The difference between genius and stupidity is that genius has its limits.
My friend had a friend work on his gas heater. The friend bypassed the electric eye that monitored the pilot light. The long story made short is my friend was blown over backwards and had his hair singed and eyebrows removed. He was very lucky the whole house wasn't blown up. Get a pro to check out your furnace.