This problem could be as a result of a number of things.I have listed a number of them that you might want to check out.
1.Low fuel pressure - supply from the tank to the HPP (high pressure pump)do you have a electric pump in the tank? Or is the HPP sucking up from the tank. The pressure should be aroung 2 to 5 BAR
2.Fuel Lines bent/cracked.Also check the fuel tank breather to see if its blocked.
3.Fuel Filter or filter head blocked/dirty.
4.Faulty Injectors. (how many miles has the engine done, if its around the 100k then you may need to replace /service)If you have excessive wear on the injectors this could result in "back leakage"which is when the waer in the injector parts allow the fuel to return back to the fuel tank or fuel system,but causes a drop in rail pressure.
5.Pressure Regulator-sensor.The regulator is normally fitted to the HPP and the sensor fitted to the rail.If either of these are faulty you will get hard starting
6.Cam/crank sensors.Check that they are not loose,cracked or damaged as they are not very expensive.If in doubt change them.
As you can see it could be a number of things, but i hope this has helped.