There's one more thing I haven't seen mentioned: timing. Read on. We've seen that the MOSFET is a type of transistor, a current valve. It lets the current go through when a signal is applied to the control point, and that happens when you push the button. The little switch itself would burn up if they passed the current through it, so they use the transistor as a stronger valve. The transistor itself is minuscule, and is mounted on some sort of heat dissipator called a "heat sink". As the current flows, the transistor heats up, and the heat has to go somewhere fast enough. If not, the transistor reaches a critical temperature and fries.
Another timing factor is that when any coil is powered, it draws more current briefly and then less. The resistance we measure is the cold resistance. If the coil gets hot enough, that resistance might stretch significantly after say a quarter second. During the initial current surge, the transistor can pop if it heats up faster than heat can be absorbed by the surroundings. Usually the transistor package itself is a good enough heat sink to absorb a short surge, and what matters more is what happens during the seconds you are holding the switch. The rating on a MOSFET transistor is normally listed two ways: max allowed surge current and max steady state current. These are just two different ways of talking about overheating. So the calculations we did based on cold resistance and a max allowed steady state current for the MOSFET transistor are not very meaningful. I don't know what type of MOSFET they use, and it may even vary from batch to batch. And atomizer/carto coils may vary in how much their resistance changes as they heat up.
But the longer you hold the switch, the more heat is building up, and unless the design is very effective at pulling the heat away, at some point the transistor will likely overheat. An automatic battery has air flowing through the switch section, so it could be designed to direct some of that airflow to cool the transistor. But we can see that there's no simple rule as to how much current (how low a carto resistance) is OK. The same MOSFET transistor might handle 3 amps fine for hours if it's mounted on aluminum with air blowing past it, and might fail after 5 seconds at 1.5 amps if the heat has nowhere to go. It depends on the build of the transistor, how it's mounted, and the (changing?) resistance of the coil.
But here's a practical conclusion. Don't hold the switch down too long, and your chances of frying the battery switch circuit will be reduced. If you keep the on-cycle short the battery itself will also thank you, as it has its own limits, that are even more complicated. I've fried a couple of generic eGo batteries with eGo Mega Atomizers, and it was while I was holding the switch (doh!) that one went "pop", and the other just stopped working. A third battery, a Joye 650 eGo battery, lost its MOSFET when a T-Atomizer suddenly became quite low-resistance, so that was unavoidable. If you can't afford experimenting with eGo batteries, use cartos/attys with a cold resistance over 2.5 ohms, and never hold the switch down longer than you have to. If you use say dual coil megas at 1.6 ohms, you might want to pulse it one second on, one second off. That's practical when the carto delivers faster than a single coil. And you can explain to spouse why it might be time for a pretty mod with a huge battery.