Sounds like fuel pressure bleeding off. Put a gauge on it and see if it drops overnight. If you don't have a gauge try this. At the next cold start don't crank the engine at first. Turn the key to position 2 for a few seconds then turn it off. Repeat this several times. Every time you do this the pump will run for a second or two building static pressure. If it then fires and runs smooth you'll know the pressure is dropping.