2000 S-Type Intermittent Start up issues

I have a 2000 S-Type that, since late October, has exhibited erratic starting issues. Out of the blue and with no prior warning, the vehicle will not turn over, as follows:
1. Ignition to START - gauges activate and dash lights – ABS, seat belt, etc. Come on;
2. Ignition to ON - system shuts down as gauges and dash lights shut down and nothing happens; no cranking noise, nothing.
I have taken the car to the dealer four times for this issue and they have replaced 1. An ignition coil and the battery; 2. The starter; 3. The ignition module. Obviously, none of these repairs fixed the issue as the Jag is at the dealer, and has been for over a week, as I write this.

On all but the third occasion of this issue, I was able to start the Jag later and drive it to the dealer. On the third occasion of this issue, the car would not start for three days and had to be towed to the dealer. On the three occasions, I was able to drive it to the dealer after it had sat for from several hours to over night.

Usually, this issue returns approximately six weeks after the previous repair was effected; however, this last time, the car refused to start he day after the dealer returned it to me (about 37 hours after I picked it up).

According to the dealer, they have called the Jaguar Tech Hot-Line to no avail as Jag has no idea what is wrong.

The dealer, currently, cannot replicate the issue; so, no repairs have been tried.

Any ideas on how to permanently fix this issue are appreciated.