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Had an issue with my 4.0 Daimler over the last week. Whenever I started it it would stumble for the first 10 seconds or so and then even out to a smooth idle and drive fine. I suspected may be a fuel pressure loss issue. I tried the repeated Key on - Key off routine and this made it start smoothly and idle fine from the get go. So that confirmed to me that it was a fuel pressure loss problem.
Except it wasn't. The fuel pump (with the Non Return Valve) is a new Walbro unit (about 5K miles ago) so my first port of call was the Fuel Pressure Regulator (original) as I have a spare in the garage. When I opened the bonnet to start the job to swap out the regulator I noticed the Temp Sensor was unplugged (I did that while trying to see part no. and forgot to reconnect it). Reconnected it and all is good again.
The point of the post is for those who have a similar issue in the future. I don't understand why the Key-On Key-Off routine made starting better even though the Temp Sensor was disconnected but it did. So be aware that repeated Key-On Key Off doesn't prove there is a fuel pressure loss.
You could have experienced 2 problems at the same time in your starting sequence
Good observations on what can be happening
On the fuel pressure there is a check valve on the fuel pump as well as the regulator up front holding 43 PSI for days
The cycling the ignition switch charges the fuel rail with the pump cycling on for 4 seconds a cycle by design
This is a way to recharge a lacking fuel rail trapped pressure
Some solutions to resolve this is to observe if fuel leaked past the diaphragm in the regulator and is noticed in the short ke manifoldvacuum attached to the inta
As to the check valve in the fuel pump , some have installed a external to the tank check valve before digging the fuel pump out
With the 2 wire coolant temp sensor , if the connector is dirty or corroded this increases resistance and on the thermistor type sensor this mimics colder coolant temperature and the fuel mixture is biased rich to the value of 8.0 on the short term fuel trim
Not until the coolant sensor ( and good wiring ) see a target value of X degrees does the ECU even look at the O2 sensors for true closed loop engine regulation