I know it’s not scientific, but as what matters it what it tastes like to me, I think I’ll stick with a blind taste test. I assume I could take it to Yale, but I don’t know anyone in the Chem department to beg a favor from 
A blind test seems pretty reasonable. I don’t trust non-blinded tasting but a few samples of a blind test seems fine. Just make sure you hold the temperature constant. And you might want to have actual blinding as well, so you can’t infer anything from the visible bubbles.
ETA: I was looking at CO2 sensors as well, and while they are available, most are designed for air quality use, so they cap out at 10,000 ppm or less. I wanted something that works up to 1,000,000 ppm…
If it never reinflates the bottle, then that means the remaining quantity of dissolved CO2 is low enough so that the the equilibrium CO2 partial pressure above the liquid is less than one atmosphere. Looking at @Dr.Strangelove’s chart upthread and assuming a 5C refrigerator, it would mean something less than 0.063532 mols of CO2 per liter of soda.
But if the container is open, then ambient air absolutely will diffuse in, and CO2 absolutely will diffuse out. It’ll happen slowly because of the literal bottleneck, but it’s inevitable. The partial pressure of CO2 above the liquid will decrease, and CO2 will continue coming out of solution; the process will continue until the amount of dissolved CO2 asymptotically approaches something close to zero.
actually in my experience, if you take warm or even room temp soda and put it in ice it goes flat almost instantly …
Found this out when the snack bar on my Amtrak train just took a can of soda out of a box and poured it into an cup full of ice … although the cup looked like the ones you see in a Motel 6 bathroom …
What do you call it when someone refers to you in the third person while talking to you?
Sure. But the rate matters a lot. It’s easy to prove to yourself that even with a wide-mouthed container, CO2 can persist without much diffusion for many minutes. With a small opening, lack of drafts, etc, it seems likely that CO2 can persist at high concentration for long periods (days).
Sample 1
Sept. 26, 1:00PM EDT
The refrigerated bottle is good and cold now. Not much to report, both bottles opened for the first time. The cold cup tasted fizzier.
“It rubs the lotion on its skin…” 
Sorry, was past my bedtime and I was berry, berry tired.
That’s interesting, as from my personal experience, doing the squeeze thing seems to make the soda go flatter faster to me.
Sample 2
Sept. 26, 9:10AM EDT
the refrigerated bottle seemed slightly more firm, and the sound of gas escaping when opened slightly longer or louder. But neither was clearly and convincingly different from the unrefrigerated bottle. The sample tasted about the same as the first sample. The cold one seems fizzier.
Science! He’s blinding us with Science! 
Seriously, thanks for doing the experiments and sharing your results.
It isn’t clear to me what you are comparing.
To be a valid comparison, you have to take the room-temperature sample and chill it before you compare. Comparing the cold sample to the room-temp while the room-temp is still warm will have many more variables that swamp out the amount of CO2.
I’m testing to determine if soda in 2 liter plastic bottles of Pepsi kept in the refrigerator go flat faster than 2 liter plastic bottles of Pepsi kept at room temperature. Not by just sitting opened or unopened, but in periodic opening and pouring some out of each bottle, reclosing them and returning the cold one to the refrigerator. That’s how people often use 2 liter plastic bottles of soda. My testing is only to record my perception of flatness in the samples because I don’t have any means to determine the actual CO2 content of the soda or any means of determining anyone else’s perceptions.
Right, that makes sense. But by taste, you can’t tell if a warm soda has retained more CO2 than a cold one if you are tasting them at different temperatures. They will have a very different mouthfeel due to temperature, not because of the amount of dissolved CO2.
Right. That could be a problem in the end. I don’t like warm Pepsi, I almost always drink it with ice. I’ll have to see if my perceptions change as volume of soda left in the bottles decreases despite being skewed by the temperature difference.
Didn’t get to post until now. Don’t think the timing after some brief minimum makes and difference.
Sample 3
Sept. 26, 4:15PM EDT
Sampling a little early to adjust for my erratic sleep schedule. Nothing special. No difference detected in bottle firmness or gas escaping when opening the bottles. Both samples tasted flatter than before. They seem to be getting flatter at the same rate.
Sample 4
Sept. 26, 10:35PM EDT
This is interesting. No difference in bottle firmness or sound of gas released when opening. However both cups of soda taste pretty flat. The temperature difference is much less significant to the ‘taste’. The cold one ‘tastes’ about as flat as the warm one.
Sample 5
Sept. 27, 7:00AM EDT
Both samples are pretty flat now, very close to the same. The cold one retains a very slight advantage. If this could be quantified then the refrigerated bottle has lost more of it’s original fizziness than the room temperature bottle. At half full both bottles are much less firm, neither less so than the other. No noticeable difference in the sound of the gas escaping when opened.
Sample 6
Sept. 27, 2:25PM EDT
The only difference between the bottles and samples is the temperature. They’re both pretty flat.
Sample 7
Sept. 27, 10:00PM EDT
Both samples are very flat. Bottles are not firm. No noticeable sound when opening the bottles.
I was going to wait to take the final sample tomorrow morning but I’m pretty sure the following conclusions won’t change:
Conclusion 1: Pepsi goes flat after bottles are opened and some poured out whether refrigerated or not.
Conclusion 2: Based on individual evaluations of what ‘tastes’ flat or fizzy, along with variations in the amount poured out over time, one could conclude that soda goes flat faster if refrigerated, or one could conclude that soda goes flat faster if not refrigerated, or that it goes flat at the same rate whether refrigerated or not.
But let’s see if one of them miraculously becomes less flat overnight before I commit to that.
Tie breaker: if you prefer your beverage chilled when you actually imbibe, then other things being equal, it seems you should refrigerate. Because refrigerated beverage doesn’t need ice to drink chilled, thus no accompanying dilution from melt.