This is a very strange problem, so I'm sorry if I describe in in a confusing way.
For the past few days, I've been playing around with NFC on my Oneplus One phone. I installed a few apps (NXP TagInfo and Trigger, most notably), and they work fine. I wrote a simple app to scan and display the ID of a tag. This was all working fine with the NFC tags I have lying around (Tag inside a water bottle: NfcV. Other tags: NfcA (I think). They're unmarked, and this is all I know about them).
But suddenly a problem started: One tag, which is inside of a water bottle, scans fine. But the other two tags I have don't. When I try to scan them, they 'break' the NFC on the phone, and it becomes unable to scan the water bottle. I have to turn NFC off and on again to fix it, at which point it scans the water bottle just fine. This problem is very consistent.
I have a Nexus 4 which was able to scan all of the above tags and display the ID, but not read or write the actual data on the tag. My Oneplus is able to read and write data to the tag in the water bottle.
I don't understand what could possibly be causing this. As I previously mentioned, the tags worked just fine earlier. I haven't updated the phone or made any significant changes over the past few days.
Phone: Oneplus One, rooted, running CyanogenMod 11S (The stock software the phone shipped with)