If the pressure in the system is marginally low, it will prevent the boiler from firing. Not sure where in the logic sequence it looks at that, so it may not even try to start when it's low. If the thing fires at all, as the water heats up, the pressure can rise, and eventually, let it keep running. Are there any error signals or anything on the controller board when this happens?
Any boiler has multiple safety interlocks, so you need to check each sensor to figure out if one of those is the issue. The installation manual is likely your best friend on this to try to figure out why they dont' want to start.
Exactly what happens when you reset the system, and what are your static pressure readings?
Are these running on LP or NG? If LP, the regulator might be a source of the problem.