problem with Baxi Solo 370?

When we put the heating on over-ride so that it should remain on until we turn off, we have the following problems. Sometimes it goes on and stays on, other times it looks like it is on i.e. the boiler has fired up and the light on the timer is on but the radiators donot get hot. Other times it comes on and just switches off after a short time. When we just put the water on, one of the radiators comes on too. We have had 2 new divertors and 1 new timer. Is there a problem with the relay board in the boiler? It is 13 years old and we have had this problem on and off for over a year. Not one engineer seems able to pin point the problem. Can you help?