I have a Reddy Heater 35. It will spray fuel & ignite but when I slide the cover back over the unit the flame will go in & out.

A worn nozzle creates a spray pattern, where a good nozzle creates a fog.With a coarse spray pattern poor combustion results in an off colorflame, . The photocelldoesn't like the color, sends a signal to the computer whichshuts everything down. That's the job of the electronics. On HSI ( hot surfaceignitor) heaters it is all about correct flame color , not just flame. The part where you write "If I remove the cover again it runsfine" is a symptom of a bad, worn, or restricted nozzle (generally).Remember- the ignitor only stays red for 5 seconds, then the flame keeps itselflit. The nozzle's pattern is a cone. Lift the lid & the pattern widens(aerodynamics) - replace the lid and the cone narrows & possibly distortsthen the flame goes out. This nozzle rule will only apply if everything is correct as far asfuel delivery applies. The pump pressure must be correct- not almost correct.Set the pressure with a low-pressure gauge that registers12-15 psi max. A gaugewith a higher scale just will not read close enough to satisfy the system. If the pressure is not correct, the aboverule will not apply. Instructionsfor setting the pressure can be viewed at http://reddyparts.com/pressure.htm. In addition, a fan can cause the same problem if damaged ormis-matched to your specific model. I must mention that any air leaks onthe pressure side (or vacuum leaks on the fuel line, for that matter) betweenthe pump and the nozzle will create a rich/lean mixture at the combustionchamber, creating an off-color flame.

Check your fuel lines and most models have a fuel filter in line. A few things come to mind one how old is the fuel? Check the screen in the nozzle assembly by removing nozzle it sits directly behind the nozzle, these corrode and affect fuel flow. While you have this tore down clean the fire-eye with windex and terry cloth rag, it may not be seeing the flame. Check the air filter at the back of the heater as well. These are common problems with these heaters.

Thanks for providing the model of your heater. Most folks don't.

Your heater has a photocell eye and a computer board (ignition control). This team monitors the flame. If the team does not like the color of the flame then they shut the heater down and that is the situation you are in. Now, you must troubleshoot & find the problem. Is it water in the fuel, incorrect air pump pressure, worn nozzle, cracked plastic cover, etc.

Read these troubleshooting tips.

You probably need to bleed the fuel line.Most likly looks like a brake bleeder valve..

flame sensor clean with steel wool usually right next to hsi should fix.

When you say the heater is coming on does it actually ignite or is the motor just running until the safety circuit kicks it off? The air pump on you heater should blow at 3.5 to 4 psi which runs up to the nozzle which is a venturi which sucks the fuel out of the tank. The motor will generally run for 20 to 30 seconds trying to ignite. If the flame sensor does not sufficient flame during the time it shuts the motor off. Check these items and let me know what you find.

the unit is working exactly as designed , the system is noticing that the unit has not fired so it shuts down so there is not a lot of unburnt fuel everywhere.
try to find out why the unit is not igniting . is the igniter sparking continually

CAD flame sensor is bad, also check your air inlet line for the fuel mix, could be cracked.

it would probably be your igniter. it is probably not producing a spark

This is a "probably". The reset button trips because the photocell fails to see a flame in the combustion chamber. That's its job.
Check the ignition device ( transformer, coil). See if 110v going in. If there is no spark coming out, replace it.
Troubleshooting tips