the immobilser will usually cut 1,2 0r 3 circuits

either igntion, fuel pump, starter, or all 3 or a mixture

if the starter is trying to start then it will be definitly battery as there isnt enough juice to get it going

batteries can go anytime, they can be fine one minute then completely dead the next

as you were doing long journeys the alternator was charging the battery up enough to last the day at stop start intervals, but left stood it went flat again

im 90% sure its battery and would be surprised if its the immobilser