Paul, got the same symptoms on a 3.0D XFS. Windscreen washers work as expected anytime if engine stopped. However when engine started, washers will operate for one cycle and will not work again until car is stopped and restarted.
Though I had cured it by disconnecting the battery for a while. Washers started working properly, but initial fault had reappeared. This has to be software related, but like you cannot find any information, or dealer that wants to try anything other than replacing pump.
Help?