Sounds as though the battery voltage is a bit low, or its on its way out
However If the immobiliser is the same as the plus 8 there are two boxes,
One is called the Spider unit which decodes the ignition key and is notorious for failure due to dry soldered joints internally, these are no longer available - but the main online land rover parts suppliers will sell you linked out plug for around a tenner .
The other (green) box is operated by the key fob, this sends a constant stream of data to the ECU, if the data is interrupted the engine dies or is inhibited from starting. There are people who will check out the box for £25 and carry out any repairs.
