I have a Glow-worm gas boiler. Every once in a while, not with any noticeable event/coincidence, it will stop "kicking in".
It does this when in a program "on" cycle. Not when the timer goes from off to on.
It does it more often around 6:30pm, but not exclusively. Sometimes we go 2 or 3 weeks without incident. Sometimes it's a couple of days.
The cure is to turn the power off, leave it a minute, turn it back on and all is good again.
Turning the thermostat higher so that it "clicks" does not make the boiler fire when it's having one of these wobblies.
I've replaced the programmer, yesterday, and it's just done it again! I tried a different thermostat previously which made no difference.