It should be quite happy for a few weeks before the battery goes too flat to turn off the immobiliser with the plip. If you are using a Cetek (and its actually doing what it should be doing -i.e. battery maintenance, then this problem should never arise. If the battery voltage remains above about 10V, it should be enough to keep the alarm set properly. The car probably won't start, but at least you should be able to switch off the alarm!
When you say that it is immobilised, can you still activate the central locking with the plip? If that is the case, what happens next? I assume key in the ignition and switch on. Does the red immobiliser LED go out? Although its one system, the car alarm has three functions. The first is to monitor any entry through any slam panels (perimetric alarm). The second is the interior sensors (volumetric alarm). If these two are working, but the third function (immobiliser) is not deactivating, then you need to be looking at the security signal between the engine ECM and the body control module. That's a T4 / Autologic job usually.
Final thought. If the battery is good, central locking works, but the immobiliser does not deactivate when the key is inserted, does the red light go off if you press the unlock button on the plip with the ignition on? If so, it could just be a faulty passive immobilisation coil. That is fitted round the ignition switch (same on TD5 Defender). If that isn't picking up a signal from the alarm plip in close proximity, then that's an easy change.
If there is no response from either key fob with new batteries fitted, then ideally it should go onto T4 or Autologic to monitor the alarm and key inputs. It would be worth doing that anyway to try and find out what's going on. As I said before, the Discovery 2 alarm is pretty bombproof and reliable. The key remotes are usually the only obvious weak point.
A good independent LR specialist should be able to sort it out. Don't waste your money at a LR dealer - its rare to find anybody there these days who knows enough about them.