On my MK1 mondy I had it was under the dash bit below the radio area, on the floor.
Some suffer from bad joints as they do get condensation inside caused by the heat of exhaust etc under car heating area where the immoby sits then cooling when you turn off etc.
I took mine out of mondy and resoldered EVERY JOINT, then spray with CONTACT CLEANER, elcetrical not glasses!!.
Then blow with air line to get rid of any residue.
Anyway did all this put it back and bingo all well, 2 years later.
It may not be the imobiliser but the KEY, especially if it has been dropped recently.
The trick is to wrap key in TIN FOIL for about 1/2 hour, then insert into ignition, turn on/off 3 times , THIS WILL DISCAHRGE ANY STATIC that has built up, it's free so worth a go, it does work on some if this is the problem, as I have done it.
tabetha