no start: engine immobilizer random issues

[the_teach]

Alrighty so i'll start this post off with a HI! to everyone here :)

A little background on my car - It is an 09 4-Door Sedan in Canada, Automatic, Power features and a/c. ( LE package i believe ). It has 345,000 Kms of roughly 90% city driving ( was a work car ). No CEL's on ( ever ). New fuel pump, alternator, MAF, throttle body, and transmission (last 3 weren't needed was chasing problem #2 below). EDIT: both keys have new batteries in them ;)

The issue: Randomly, could be twice in a month, or once every 8 months the car will not start. Previous owner had the code pulled at the dealership - who couldn't figure it out - and it said engine immobilizer ( anti-theft ). The weirdest thing though for this problem is that after sitting for 30min - 2 hours the car will start again and act like nothing ever happened. No strange lights on the dash or anything. Wouldn't know it ever happened. Also it will not do this on a dead cold start, only after it has been shut off for half to an hour.

This issue is getting seriously annoying as it happened again. Looking for any and all leads into it.

Second Issue: If you drive at a constant light acceleration from 40km to 70km/h the engine surges ( tach ) up and down by a few hundred rpm and the car moves with it. So far changed MAF, Throttle Body, and as of the advice of others - the whole transmission ( they thought it was a sensor on it ). Any ideas here would help too. I'm personally leaning towards possibly an 02 sensor.