When 55 Watts load was connected,it was not 55 Watts. The cold filament resistance is lower and initial power surge may be four times higher for few milliseconds. A current sense circuit copes with this situation by reducing pulse width even if voltage go down. In your schematics you are using two resistors R38 and R83 in parallel equels to .01 ohm. That means 100 ampers through these resistors will produce 1 volt. At that poin LT1245 will try to keep current below 100Amps because its current limiting function activates above 1V equals 1200 watts load. Two .1 ohm resitors will limit load above 240 watts
When there is overload on power line 12V, it may reduce to 6V due to resistance or loose connection. LT1245 has a "low voltage lockout" function that means it stops operating below around 7.5V but then starts again near 8.5V.(when oscillation stops,current is lowered, voltage rises on power line, oscilation starts again) Random oscillations generated causes further overloading and saturation of core. Diode charges capactor to peak and when volt becomes less for a short time(glitch), capacitor provide voltage required( same as filter capacitor does in ac rectification). This can also assist filter capacitor on power rail providing more filteration to control circuit.
Sensing output current acts more rapidly, it is ignored in your schematic.