Why can't CO$_2$ mix back with the liquid after a soda bottle has been shaken? If you shake a soda bottle before opening it, and then open it, you get the fizz.
That is the compressed CO2 releasing to the atmosphere which is at comparatively low pressure value.
Two questions (related)


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*Why does shaking a bottle make the compresses gases un-dissolve?

*Why can't the gases dissolve back into the liquid?
 A: I cannot see, above, the correct answer to the first part of the question. They all have the second part right. 
The first part: Why does shaking the bottle make it fizz when you open it? 
The gas is in solution in the closed, unshaken bottle. The solubility of that gas in that liquid at that temperature and that pressure dictates the saturation level of the gas in the liquid. Any more gas than that and it bubbles out, increasing the pressure inside the closed bottle and forcing more gas in solution thus reducing the pressure. An equilibrium is reached.
But why does shaking cause a problem?
Because when you shake it, you slosh the contents around. The liquid flows quickly from one end of the container to the other. As it does so, it flows fast enough to become turbulent. In the turbulence, the curlicues, the intricacies, the eddies and the complex flow there are many locations in the liquid where the local pressure is forced lower than the saturation pressure. This is because any packet of liquid that is accelerating in any direction will leave a low pressure zone in its wake.
When the pressure is forced below the equilibrium level, the gas (given sufficient nucleating seeds) will come of of solution instantly given that the operation is occurring in the bulk and gas bubbles can be created anywhere in 3D.
But when the gas wants to go back into solution it is severely limited by the relatively small surface area of the liquid in the neck of the bottle. There is only a tiny surface available for gas transport through the liquid/air interface. We are severely dissolution rate limited. It can take hours for a shaken can to quiet down. It can be hastened by chilling as more gas can always be dissolved in a cooler liquid. 
A: This is what I think that happens. The bottles with the soda have the liquid inside under pressure. Under these conditions you have an amount of CO$_2$ dissolved in the liquid. If you shake it then it will make some bubbles but not a lot and it will return to the previous state. If you don't disturb the liquid and open the bottle, then the pressure will drop to atmospheric levels. The dissolved CO$_2$ in the liquid is in a grater concentration that the liquid can hold for that pressure. But there are no evaporation seeds for the bubbles to form. It is a similar thing with the superheated water, where you have crossed the threshold for a phase transition, but you need impurities to initiate the process in the liquid. If you disturb the liquid it will produce bubbles. If you first shake the bottle and then open it, then the agitated liquid will form bubbles of CO$_2$ with the pressure drop. Now, once you have reduced the pressure on the liquids surface, there is no way to put the CO$_2$ back in to the liquid, except for increasing the pressure again.
A: For the first question, I'll give an analogy that I hope illustrates quite well what is happening here. Imagine you have a ball on a floor. Now an earthquake comes. If its not too destructive, the ball will just roll and maybe bounce but after the earthquake is over, it will still be on the floor. Now imagine that you would put that ball on your desk (so you use some work to overcome gravity). What will happen after the earthquake? Well, it's pretty certain that the ball will fall to the floor and all your work will go uselessly away in the form of heat (that is produces when ball hits the ground) and the entropy of the system increases (as it should by the Second Law of Thermodynamics).
Now, it should be pretty obvious that if you replace ball in the above with $CO_2$ bubble, work to overcome gravity by work needed to compress the bubble and earthquake by the shaking, you have precisely the same situation. So the system is in an unstable equilibrium and any big enough perturbation will bring it to the stable equilibrium.
Your second question is either trivial or wrong, depending on how you meant it. If you meant it in the way why doesn't $CO_2$ compress itself back then the reason is the same as why balls don't hop up on your desk when left to themselves. They don't have energy for that.
If you meant it as just dissolving, then as a matter of fact, they do. Both water and $CO_2$ molecules are both in the volume of the liquid and the air. For example, there is always some water vapor above the surface of the water. The exact concentration depends on the volume and pressure in the bottle, but except for that it is constant and non-zero. But the concentrations in the stable equilibrium case are very different from concentrations in the unstable (compressed) case and it is always preferable for the system to increase its entropy thereby moving from the unstable to the stable equilibrium.
A: Water can dissolve a certain (low) quantity of CO2. To create this "refreshing" effect (that is when all the nerves in your gullet fire because they have the impression to being dissolved by an acid :-)), a lot more CO2 is dissolved in the soda.
But the liquid can't keep so much CO2. To keep the CO2 there for a certain time (say a couple of months), the bottle is under pressure. This way, the CO2 molecules will spread evenly in the liquid. That only works because the liquid can dissolve some CO2 in the first place. It wouldn't work for something that doesn't dissolve (rock, oil, ...).
A liquid can't be compressed, so the volume of the water doesn't change when you open the bottle. You will get a little bit of fizz from the small amount of air on top of the liquid. But most of it will come from the CO2 which isn't kept in the liquid by the pressure.
Why does CO2 dissolve? It actually forms a (very weak) molecular bond with the water. This way, all the molecules can reach a lower energy state (the water forms "pouches" for the CO2 molecules and they "rest" in there unless disturbed).
This is very fragile because the water doesn't really want to dissolve so much CO2 -- it just has to because of the pressure under which this happens. Now when you share the bottle, you disturb this fragile balance. The CO2 molecules move and start to form tiny gas clouds that tend to absorb each other (because they like each other more than the water): You get bubbles.
If you don't open the bottle and wait for a few days, the water will dissolve the CO2 again. This is slow for many reasons. First of all, the water doesn't really want to. Second, no one mixes the water, so the part near the surface has a high saturation and that disperses very slowly through an undisturbed liquid. Mixing the water would be bad, even.
In the production plant, a nozzle is inserted into the bottle and the CO2 is released near the center of the liquid. If the bottle wasn't sealed, the CO2 would quickly evaporate. But since it is sealed, the CO2 spreads evenly in the liquid (so actually the water dissolves the CO2 bubbles, not the CO2 itself).
This is the reason why you only get a small fizz when you buy a bottle since it has been shaken a lot before it arrived at your place (moving to a storage, on a train/truck, loading/unloading, stacking onto a shelve, carrying it home, etc).
