[Galaxy S III Q&A, (US Carriers)] ascsa:
After turning the screen on (and unlocking it) ... the tag will be scanned again ....

and for the battery drain ... i had a look at the logs on my international gs3 while taped to a tag ...a lot of log messages and probably cpu activity while taped to a tag, repeated approx. every 150 milliseconds ...

Have a look --> this is just 1 second in the log .... and it´s repeated as long as the tag is taped to the device ...

07-12 02:47:25.057: D/NFC_LIST(10575): Allocated node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.057: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.057: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.067: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.067: D/NFC_LIST(10575): Deallocating node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.192: D/NFC_LIST(10575): Allocated node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.192: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.192: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.202: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.202: D/NFC_LIST(10575): Deallocating node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.332: D/NFC_LIST(10575): Allocated node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.332: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.332: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.342: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.342: D/NFC_LIST(10575): Deallocating node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.467: D/NFC_LIST(10575): Allocated node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.467: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.467: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.477: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.477: D/NFC_LIST(10575): Deallocating node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.607: D/NFC_LIST(10575): Allocated node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.607: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.607: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.612: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.612: D/NFC_LIST(10575): Deallocating node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.672: D/KeyguardViewMediator(2098): handleTimeout
07-12 02:47:25.742: D/NFC_LIST(10575): Allocated node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.742: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.742: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.747: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.752: D/NFC_LIST(10575): Deallocating node: 0x17c6f28 (0x5d5efbf4)
07-12 02:47:25.877: D/NFC_LIST(10575): Allocated node: 0x1702e60 (0x5d5efbf4)
07-12 02:47:25.877: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence()
07-12 02:47:25.877: D/NFC JNI(10575): phLibNfc_RemoteDev_CheckPresence() returned 0x000d[NFCSTATUS_PENDING]
07-12 02:47:25.887: D/NFC JNI(10575): Callback: nfc_jni_presencecheck_callback() - status=0x0000[NFCSTATUS_SUCCESS]
07-12 02:47:25.887: D/NFC_LIST(10575): Deallocating node: 0x1702e60 (0x5d5efbf4)

EDIT: Don´t get me wrong, having NFC enabled, usually doesn´t make a relevant difference for your battery life ... but keeping a tag permanently attached, seems to have a much higher impact ...