Cranking and taking several seconds to fire up is unlikely to be a sync problem. The immobiliser code from the BECM to the engine ECU is sent from when the ignition is turned on to position II - so if it's in sync, then the engine ECU will allow starting from the first turn of the key - there isn't any delay in the immobiliser code being sent.
Likewise, if it goes out of sync, then this is just something that will happen - it isn't a moving part (for example) where wear over time will cause it to slowly fail. The sync issues are generally sudden, with no warning. The only exception to this (that I can think of) is an intermittent connection in the wire, so the signal doesn't get passed properly.
From memory, there is only ONE connector that the immobiliser wire goes through (other than the BECM and engine ECU connectors at their respective ends) and that is the round connector under the coolant tank. It could be worth checking this for corrosion on pins etc - though it is usually a pretty well sealed connector.
Taking longer to crank and start could be a sign of numerous things - and I'm sure someone with more knowledge on the diesel engines will be able to give more info on that.
Getting the sync checked is a good place to start, because without that being done, nothing will happen and there's no way of getting it running. Once you know it should start (from an electronics point of view) then you can work on any other problems.
