ok it may well be a weak pump or you may be losing your high pressure from somewhere else.Right when the vehicle doesn't start get a multimeter on the rail pressure sensor(the x3 way red one on the rail) .one pin is 5volts feed from the engine man ecu ,ones a earth,the last one if the output from the sensor ,this is the one we need .At cranking the output should be
1.2/1.3 volts this then we prove the sensor is ok.With it still in the none start state on top of all the injectors you will have rubber leak off pipe .(On all peugeots number 1 cylinder is the flywheel end) On all injectors (EXCEPT CYLINDER 4 INJECTOR) the leak off pipe has 2 outlets one to the left,one to the right.Start with number 1 cylinder injector to the right of it ,it will have a very long return pipe back to the main fuel return pipe ,pull this off from the injector and clamp it off .then on all the other injectors pull of the rubber leak off pipes ,with all the pipes off get someone to crank the engine over then you should get 1/2 drops or slow dripping out of ALL the injectors .check that no injectors are pissing out if one is thats where you are losing your high pressure from .If 1 injector is faulty or more they stand out like a sore thumb .Ive known one to two injectors max to be faulty but no more than this.This is where you may be losing your high pressure from,as it can mask a h/p pump problem which has caught out a few peugeot technicians.... all the best mark