Why am I having trouble starting my Renault Clio - sometimes?

I have an S reg Renault Clio. Last week I dropped my daughter off somewhere: car went fine. Half an hour later, car wouldn't start. Turned over but wouldn't kick in. Tried 10-15 times. Walked to pick up daughter. Walked back. Car started on second attempt. Called garage out next day. Car started fine so garage couldn't work out what was wrong. Two days later, same problem: stranded somewhere with kids. By time breakdown service came, car started again. Stopped off en route to pick up son; left engine running, engine cut out and wouldn't start again for half an hour. Help!! What do I do now as mechanics seem unable to diagnose??