The thermostat that controls the water temperature may be defective, of the printed circuit card is going bad. Working on boilers can be a dangerous business, these instructions are appropriate to a qualified and licensed boiler service person.
to determine which problem might be the case , set the boiler water temperature control up to a maximum of 170F if it is not already there and tell me if the boiler gets over 135F or not, if it does, then the thermostat is bad or if it is an electronic sensor type, the thermistor sensor attached to the thermostat may be bad.
It is also possible that the high temperature safely limit switch is tripping, look for that and tell me if it has a red reset button on it or not... if it does have the reset button, it will not be the problem since you are not having to reset it to get the boiler to fire again.
If the boiler still cuts out between 122 and 135F then the printed circuit board is likely the problem.
In that case we can do a heat stress test on the printed circuit board.
Use a hair drier to slowly and gently warm the card to 120F(warm to the touch but not hot and not over140F)... if you get any change in behavior that means the card is bad...
A micro crack has opened in the printed circuit at a solder joint, or inside its CPU in that case .... or a short circuit has developed as the card expanded when you heated it.
Constant expansion and contraction as these electronics heat and during their duty cycles over the years is what wears these cards out.
It is also a good idea to replug all of the connections in the unit,that burnishes any oxidized terminal connections and will sometimes solve the problem, especially at the printed circuit card and in any sensor molex connectors. Do that with the power off to the unit of course.
Let me know what you can find, we can go from there without a time limit.