The answer is that eventually all trace of the soda would be gone because there are only a finite number of atoms of “soda-stuff” and eventually you’ll end up with a situation where there’s only one molecule left, which - assuming that wasn’t the water part of soda in the first place - will have a 50% chance of being in the half that’s removed before the next dilution step. Theoretically it could survive infinitely many rounds of this, but the chance of that is basically zero.
How many times is that though? For a litre of soda, the lower bound is about 85. A hundred ought to be more than enough. (And 300 times would be enough to dilute the entire observable universe assuming it was soluble in water, so that’s a reasonable upper bound.)
You’d almost certainly stop tasting the soda quite a while before that though. After 20 dilutions you’re into parts per million soda to water.
Things become more complicated if you replace the soda in this experiment with holy water. It seems to be agreed that 50/50 holy to regular water remains holy, but after that, some believe that dilution can be repeated forever (presumably being left to sit for a while after that step) while others claim the holiness disappears once the dilution goes beyond 51%, regardless.
If DOSBox runs on one, then the old DOS-based Windows versions might work. But then, they didn’t keep much in System32, where they even had it at all.