Welcome to the site..

The intermittent loss is in question..

The first questions would be, the new cap installed pressure rating is? and is double gasket/sealed for the overflow system?
Looking into the rad neck, any issues with the caps seat area? Pits, hairline cracks etc. Same with the radiator cap flange.
What’s the temp gauge doing/showing’? (Normal, any high or over temp ?)
Coolant reservoir level remains the same?, should be a level rise. Hose is open, no tank inlet restriction or plugged..
If the cap is correct pressure and type, no issues within the rad neck, and an open unrestricted recovery system, although an event purge would/should be conditional,, it should obviously be fully contained within the recovery tank until spill over, even if incorrect cap pressure. If the recovery system is plugged,, and the cooling system goes over pressure it would still purge from the neck.

That said,, and all cap type/pressure correct, and any neck related damage and recovery system flow double checked.. It should not exhaust coolant to the outside, only to the tank, possibly tracking from high pressure releases if cause. More so if the reservoir level is high.

“If over temp”,
Generally if a radiator core restriction , thermostat, fan clutch, water pump, or any type of circulation issue, the temp will spike or can remain high or off spec.. A head gasket leak etc. into the cooling system can aid in conditional over temp events, over pressurizing it with combustion gasses into the cooling system and exhaust coolant out the cap w/without high temps.
But again,, should be contained in the recovery tank to the point of capacity spill.
If during times when it doesn’t purge coolant for days, (or during) any steam on start up or running from the tail pipe? or does the coolant level drop or need topping off frequently?

Checking the top radiator hose, and then the lower hose, (carefully) by hand or better yet a non contact temp gun, temps should be relatively close in temp if coolant is flowing normally. If the lower hose is noticeably cooler/cold then you may have a flow concern. Running the engine in place, A/C On etc. and a rad thermometer monitoring temps may give a first step indication of a healthy flow and base temp range held.. As well as, combustion leaks into the cooling system generally produce tiny bubbles and may be seen monitoring flow/temp, and once the cooling system is pressure cap maxed it will purge the coolant, or, after some hot soak time, on a restart you may see a puff or more of white from the tail pipe.. If so, generally will show deposits on the spark plug/s. May not be your issue, gasket, cracks etc. but notable with coolant loss events.. More so if no indicated over temps, and no cap/neck issues, and the recovery system is functional..