Is it better to stand up or lay down a fizzy drink bottle to retain it's fizz. Or is it better to compress that bottle so that no air gap is left in the bottle? I have had arguable success with the last method - any thoughts people without having to put compressed air in it?

I'm game for a test, but the collapsing bottle method has a flaw: Escaping gas from the soda can partially re-inflate the bottle, giving room for more gas to escape. The best bet, so far as I can imagine, is to keep the pressure on; though how I'd do that on a regular basis, I can't imagine. it's not like most of us just happen to have a bottle of CO2 laying around the house just for this purpose.

maybe if you squeeze the bottle AFTER you cap it... (and hold it squeezed)

Agree with the "if after bottle was squeezed it expands" but unless it is shaken it seems to to stay squeezed. I also like the keep the bottle squeezed. I am now in the testing phase with large bottle of coke clamped by a quick grip clamp and some jack daniels. Wife hates these experiments more than if I use the dishwasher to clean engine blocks. Keep the comments coming.

Some soda dispensing systems use what is called "premixed" soda. This is just large tanks of soda ready to drink. It's not like the kind of systems that use syrup that is mixed with carbonated water as it is dispensed. In order to keep the premixed soda carbonated, it is kept under a pressure of around 25 to 30 psi of CO2.

I think Master Booger is correct. If you could keep the sealed soda bottle under 25 psi of CO2 pressure, it should keep the soda carbonated. One method would be to place a very small piece of dry ice in the bottle. This could be dangerous though if you used too much dry ice. You would need just enough to raise the pressure in the bottle to 25 psi. We all know what happens when dry ice is put in a sealed soda bottle. While testing bottles for the bottle rocket myths, the MBs found that the pop bottles exploded at around 90 psi.
.

In england we can get 120psi into a standard 1.5ltr pepsimax bottle. Although that was 16 years ago and bottles have probably got thinner with the credit crunch. They seem to shatter at the base Again the wife hates these kitchen experiments as does/did my cat.
I suppose the crux of the debate is at what external pressure does the coke/soda lose fizz when undisturbed?

The coke should lose fizz unless you're keeping it stored under several atmospheres of carbon dioxide - enough to keep it at equilibrium. Me, I screw the top back on, hard, and reestablish the seal.