02 Vue Starting Problems

We have a 2002 Saturn Vue that intermittently won't start. Over the last 6 -weeks it cranks over but won't start at times. The ignition relay has been replaced and after market security system has been removed. The no start situation may occur after sitting for a day or a couple hours. When it won't start we keep checking every so often and eventually it starts immediately with no assistance. Any ideas as to what to check?