The somewhat obvious answer is that there's likely a problem with your coil or how it's connected. That's a big range to be jumping; I'm pretty new to building but I've always heard to aim for .2-.3ohms either way off your goal and certainly you want it more stable. I'm not the first person who should be troubleshooting this, but the first thing to check would be that your post screws are tightened as far as they will go without cutting the wire.
Is it actually reading just .6 and 1.2-- as in one or the other-- or is it sometimes reading resistances in-between? if it's one or the other, then I'd really think one of your post screws is loose because in that case it would seem like it's sometimes only reading one coil as a single.
Is it a new atomizer?