Heat quits only in deep cold, tank has fuel. Fuel thickening in extreme cold is starving an oil burner — the classic coldest-nights failure, and a fuel-system problem rather than a boiler problem.
Burner lights, roars, then quits or locks out. That is the safety chain doing its job on a genuine burner fault — nozzle, electrode, filter, or flame-sensing. Repeated resets without finding the cause risk a chamber full of unburned fuel on oil and hide a worsening ignition failure on gas.
Gauge sinks week after week on a sealed system. The sealed side is losing water: an expansion tank that has lost its charge, an auto-fill valve feeding or starving the loop, or a slow seep at a fitting. A healthy cold reading sits near 12–15 psi.
One cold radiator or one cold side of a twin. Distribution, not the boiler — bleed the radiator, check the riser valves, and only then suspect balancing.
Bills climbing while the house still heats. Sooted heat-exchange surfaces or rapid cycling are burning fuel for no comfort.
Sorting the symptom this way is what the a phone conversation about symptoms call does with you — the dispatcher is not diagnosing over the phone, just making sure the right person arrives with the right tools.