It's very unusual for a resistor to fail - you may indeed have failing resistor(s) but you can always spot a bad resistor - they get too much voltage and burn - they first go black and then open circuit.
Capacitors by comparison are very prone to failure - they don't like heat and boilers get hot.
Consider also that the flame might be weak due to a blocked jet or that the detector may be placed in a cold spot towards the centre of the flame.
A failing resistor is your least likely cause.
Although not about your boiler - this article...
http://kaijaks.co.uk/blog/nick/2008/02/10/dodgy-old-boiler
Gives some idea about failing capacitors.
Good Luck...
October 2016