I would suspect the electo-mechanical mechanism that the brake actuates when depressed that unlocks the Park function.

 

I till wouldn't dismiss the switch at the brake pedal, if it is staying engaged and keeping the shift lock active the whole time, that could be why it stops working after a period of time, because it gets hot and sticks...
Just spit balling the idea....

 

Same thing happened to my 2011 Chevrolet Suburban, I called my mechanic who told me there is a shifter cable below transmission box and need to be placed in position because it starts slipping when worn out. I could do it with the help of my son and his friend. Took the car to his shop and he said one of the cables gone bad. Went the to dealer shop but had to buy two, one was upper and another one was lower cable because they sell it in pair. The mechanic replaced the cables and it's been a week now so far no trouble as I drive 100 or more miles per day. The part # it says on the invoice is SL-N-CABLE (04047-CT) and is the same part #for both the upper and lower cables. The cost of cables is not much. One may have same problem but I'm not a mechanic so your car may have some other fault. You may suggest your mechanic to check the shifter cables whether they are worn-out. I also checked the brake switch which was working fine and is so till today and in fact I had replaced brake switch a month ago by the same mechanic.
Thanks

 

I have a 99 suburban and it started not being able to get it out of Park. I discovered that if I turned the ignition on so that the panel lights come on and then back it off slightly so that they all go off, I can then shift it out of Park. But backing it off means the engine is not running anymore. But It will start in Neutral so I can use this procedure to move the shifter to neutral and then start the car. Does anyone know if there is a separate switch on the ignition key module that controls this or do I need to replace the entire ignition mechanism?