Problem with car starting

Hi. Recently my car has not been turning on first turn of the ignition. I generally have to turn the ignition, turn it back off and take the key out, then turn again and the car starts fine. When first trying to turn the key, the engine seems to just tick over without starting. Once it has started on second turn of the key it drives completely fine, but when the car has stopped and cooled down for around ten minutes the problem happens again when trying to turn the car on. I have tried to have this fixed a couple of times by mechanic, but does not seem to be able to fix it. Do I need to see someone other than a mechanic to get this fixed?