I had the same problem and just like you, my system also has a 3way valve.
If your valve has a "bump" on the cover, it is possible to remove the head and leave the system full-no need to drain down. In my case the valve was an old and bump free, so to replace it i had to drain the system. It is a simple job to replace and you can buy parts or service kits for these valves. So my money is on this valve - failed.
Good luck.
pete
I reckon the valve has a faulty micro switch and can't deliver power out through the orange wire.
In mid position CH and HW function (the cylinder stat providing power)
Whe HW satisfied valve moves to CH only the power to fire boiler now comes from valve (but not if micro switch at fault)
By running off hot water, once again there is demand for both HW and CH so vale drops back to mid position and boiler now works because power now comes from cylinder stat again.
Alternatively the valve may not go beyond mid position due to other micro switch, so when HW is satisfied boiler just stops and will not start again till the cylinder stat kicks in again. This is achieved either running off hot water or altering the stat setting.
Which ever it is?, a replacement actuator head will solve it
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