To my understanding the carbonated beverage loses its $\ce{CO2}$ content as gas bubbles which gives the drink its 'fizziness'. The loss of $\ce{CO2}$ occurs due to the low solubility of carbonic acid formed during carbonation resulting in an excess of unreacted $\ce{CO2(g)}$ which is trapped in the container when bottled and escapes when opened:
$$\ce{H2O(aq) + CO2(g) -> H2CO3(aq) + CO2(g)}$$
Temperature and volume of the solvent play a critical role in the solubility of matter.
Would the decrease in temperature and slight increase in solvent caused by the ice cube being added to a carbonated beverage exposed to air cause the solution to remain 'fizzy' for longer than the same solution at RT°C with no solvent increase?