This is somewhat nuanced topic on the three different kinds of systems. Three types are no external tank (air gap), recovery tank, or expansion tank (basically providing an air gap but in a separate higher tank than the highest point in coolant system).
Basic physics is coolant expands as it gets hotter and drives a need for more volume. In an air gap system (no tank) the coolant expands and squeezes the air (easy). In a coolant recovery tank system, the liquid expands into the recovery tank and when the engine cools, it “pulls” the coolant back to radiator. In an expansion tank system the coolant expands, goes into the expansion tank, and squeezes the air in the expansion tank (easy).
The advantage of the recovery and expansion tank systems is they minimize the remaining air in the system.
I did some research on density changes of coolant over temperature changes and for a 50/50 system with a 15 psi cap, I came up with about 7% change in volume. For a 16 quart system, thats about 1.1 quarts.
So, for a no tank system it needs about a quart of air to not burp coolant, or the recovery / expansion tanks needs to be the right size (I’m ignoring the growth of hoses)
Getting back to OPs issue, it seems to me that it should only burp some number of times until it created enough air gap. So unless he added coolant, or it got hotter than what worked for the baseline air gap, it shouldn’t continue to burp.
Note that radiator caps have different designs depending if they are meant for a recovery system (those have a feature on bottom seal that lets the radiator suck back fluid as it cools.
The graph is specific gravity vs coolant temperature for a 50/50 blend and shows about 7 percent change from 50 degF to 265 degF.