This might be of no help...yet, but my 03 m45 used to do that in the winter. It was not a daily driver, and when I unlocked it after a long break the first attempt was like you described - key turns all the way but doesn't seem to catch. The battery was about 10 years old and was eventually replaced, but it was good throughout this period. I did not drive the car often enough to chart any specific trends.
Enter the 05 Jaguar Xj8 this summer; never happened before. The 2nd time it happened, I noticed I had unlocked the doors, quickly got in and almost simultaneously attempted to start the car. Same thing here - it wouldn't respond to me turning the key back to off then on, but it started like normal when I pulled the key out and reinserted it. Security interlock on a timer?
The 02 qx4 used to do that over 75% of the times we attempted to start it and although I had read about the ignition cylinder sometimes developing some slop, this one turned out to be due to a worn key. I made a copy that had sharper edges and that problem went away.
... hopefully, sometime soon we'll make sense of your situation.