It could be a case of a failed thermocouple, one that senses that the flame is on so gas can be allowed to continue to flow. In any case you will best call in a technician.
Karl is almost certainly right. The thermocouple is a device designed to cut-off the gas if the flame blows out. Pushing in the knob when you light the gas bypasses the thermocouple; when you release the knob and the thermocouple is faulty the cooker thinks the flame has blown out and turns off the gas.
Ours is often like johnk's as in much of the time when the wife turns them on they go off when she lets go of them but not if I do it. It could be that not enough pressure is being used. It does wind her up though.