CD Player always starts at track 1

I have an OEM head unit with a USA-SPEC "plug and play" cd player in the slot at the bottom of my console.

The issue I have is as follows:

When I get into the car and I turn the key a couple of notches, the cd player continues to play from when I last turned off the car.

But if I were to start the car, the CD player resets back to CD 1, Track 1 and begins playing from there.

Prior to this USA-SPEC cd player, I had an OEM cd player which also did the same thing.

Is this a known issue? I apologize if I am bringing up a known issue but a search yielded no hits for me.

Is there a work around? Or am I stuck with this?

My suspicion is that when the car starts, it somehow disconnects the cd player for a long enough time that it loses its memory of the current location of the CD and Track. is this correct?

Any help would be greatly appreciated. Thanks.