From your descriptions I will assume that your controls include a common type of two port (in and out) zone valve.
When the thermostat demands heat it does so by providing power to the zone valve. Inside the zone valve (almost certainly all of them) is a small motor which turns a spring loaded cam which in turn is fixed to the valve spindle. As the cam/spindle turn so the gate/barrier within the valve turns and opens the waterway. Once the cam reaches the very end of its travel it trips a micro switch.
The micro switch energises both the boiler and the pump, the boiler comes on and the pump drives the heated water toward the radiators. Once the thermostat is satisfied that the set temperature has been reached, it cuts the power to the zone valve motor which allows the cam to return, cut the power to boiler and pump and close the valve - until next time.
The motor is a synchronous motor which is something rather special. It exerts a certain amount of torque on the cam/spindle even when the cam/spindle has stopped rotating, in order to keep the valve open and the micro switch closed. However, with age the motor can lose torque - this is not wear as we think of it but more a form of deterioration. It is possible that the micro switch is closing initially but then the cam slips, perhaps back and forth. Ultimately the motor may not even make it to throwing the micro switch. The motor is easily replaceable, readily available and not at all expensive - replacing it saves replacing the entire valve head.
It is only possible to systematically go through the checks which should reveal the problem within two hours at most by being on site. I still think the boiler is not the prime suspect and I would go straight for the controls - a crucial tool would be a multimeter to follow the electrical circuit's behaviour. I would first eliminate zone valve problems because it governs everything. From/with/at it one can establish whether all the other elements are being switched on and when energised whether they respond correctly.
bhg correctly pointed toward the zone valve and the lever on it. It is possible that the lever moves but still does not complete its normal travel. It is just possible that moving it manually and locking it in position at "on" the boiler and pump are not being reliably/consistently energised, only an electrical check will tell for certain.
It might be the synchronous motor, it could even be the micro switch, not to mention simple electrical faults (contacts/continuity). It is possible that some obstruction in the waterway is preventing the valve from fully opening and therefore preventing the cam tripping the micro switch. This can be a case of a hunt for a needle, but the haystack is not so big.