Ducted Heating won't function when it's windy

We have a ducted heating system which is located beneath the floorboards in the void created as the house is built on the side of the hill. It seems that when the weather is windy and/or really cold the system doesn't function properly. It heats for a while then cuts out. If I reset it ie turn the system off and leave it a few seconds until the controller stops calling for heat and then turn it back on it fires up again. This cycle is repeated constantly. I'm fed up with turning the controller on and off. i can't get the problem to replicate when the plumber is here. We have recently replaced the circuit board on the heater.

Can anyone suggest what the problem might be?

Sounds like the flame might be blowing out. When you turn it off and then back on it relights.
The fix might be a bit harder. If you have not had the burner cleaned it could be worth doing. Another suggestion is to see if you can protect the unit from the wind.

Please note I am not a gas fitter and the above is just guessing. I also do not know what type of unit it is and whether it has a pilot light or an automatic ignition system.

Before you turn it off and on again. Go outside and see whats still on.
See if the pilot is still running or main flame and or fan.
Get someone else to turn it back on and see whats happening. Maybe all the flames are out and the turn on is relighting the pilot as suggested ealier. Pilots lights are known to get one spec of dirt in them and then fire weakly. Usually they can push a small wire down the end (when its off) to try and push dust or dirt out of the way.
To do properly, remove either the tip of the pilot feeder and blow clean in opposite direction but only attempt if your super confident you can (my old man was a heating engineer so he showed me how to do it)

If its always about the same time to turn off (like 10 mins), maybe there is a short on a circuit and when it heats up its cutting out (I know you said you had board replaced).