[AT&T Samsung Galaxy Note I717] darkspr1te:
When you say 'internet', can you expand on that, do you mean LTE, HSDPA, WiFi, reverse tether , this is important.

Your imei is actually stored in nvram and not in /efs as in xynos based phones, how ever you do still have a efs for wifi/bluetooth and a few other syamsung bits.

Have you changed anything via the phones service menu dialer code , maybe enabled a data connection thats not compatible with your rom?

have you looked at your logcat when this happens to see if anything obvious shows like "Super turbo internet booster running, error, reboot"

Note, dont paste logcat logs direct here, use pastbin.com or attach as file.

Have you tried a factory reset ?

have you tried a factory reset/fresh rom install

repartition via tha pit file is dangerous and can brick your device and very few people recover imei/efs data this way, if anything they loose it for good,

it's like "um ive lost data, let me format the drive to get the data back"

if anything it's more like your trust zone is damaged, or your running the wrong modem or patched modem.

if you want to know

Your pit file is also on your device,

Adb shell
dd if=/dev/block/mmcblk0p11 of=/sdcard/shv-e160k.pit bs=512
Exit
Adb pull /sdcard/shv-e160k.pit

this is also how another user can copy theirs

this goes for all partitions

Device	Boot	Start	End	Blocks	Id	System Type - Text Name of Id	Partiton Name	File to restore from backup	file to restore from firmware	Known functions – purpose
/dev/block/mmcblk0	0	1	mbr	mbr	mbr.bin	list of whats stored where
/dev/sdc1	1	204800	102400	c	W95 FAT32 (LBA)
/dev/sdc2	*	204801	205800	500	4d	QNX4.x	SBL1	sbl1.mbn
/dev/sdc3	205801	208800	1500	51	OnTrack DM6 Aux1	SBL2	sbl2.mbn
/dev/sdc4	208801	208801	0	5	Extended	EXT	ebr.mbn
/dev/sdc5	212992	213991	500	47	Unknown	RPM	rpm.mbn
/dev/sdc6	221184	225279	2048	45	Unknown	SBL3	sbl3.mbn
/dev/sdc7	229376	234375	2500	4c	Unknown	ABOOT	aboot.mbn
/dev/sdc8	237568	258047	10240	48	Unknown	BOOT	boot.img
/dev/sdc9	262144	263143	500	46	Unknown	TZ	tz.mbn
/dev/sdc10	270336	271335	500	5d	Unknown	SSD
/dev/sdc11	278528	279527	500	91	Unknown	PIT	Shv-e160l.pit
/dev/sdc12	286720	307199	10240	93	Amoeba	PARAM	param.lfs	Echo 3 > /dev/block/mmcblk0p12 cancels recovery
/dev/sdc13	311296	511999	100352	c	W95 FAT32 (LBA)	MODEM	amms.bin
/dev/sdc14	516096	522239	3072	4a	Unknown	MSM_ST1	efs.img
/dev/sdc15	524288	530431	3072	4b	Unknown	MSM_ST2
/dev/sdc16	532480	538623	3072	58	Unknown	MSM_FSG
/dev/sdc17	540672	741375	100352	8f	Unknown	MDM	mdm.bin
/dev/sdc18	745472	751615	3072	59	Unknown	M9K_EFS1	efsclear1.bin
/dev/sdc19	753664	759807	3072	5a	Unknown	M9K_EFS2	efsclear2.bin
/dev/sdc20	761856	767999	3072	5b	Unknown	M9K_FSG
/dev/sdc21	770048	790527	10240	ab	Darwin boot	DEVENC	enc.img.ext4
/dev/sdc22	794624	815103	10240	60	Unknown	RECOVERY	recovery.img
/dev/sdc23	819200	839679	10240	94	Amoeba BBT	FOTA
/dev/sdc24	843776	3911679	1533952	a5	FreeBSD	SYSTEM	system.img.ext4
/dev/sdc25	3915776	8114175	2099200	a6	OpenBSD	USERDATA	userdata.img.ext4
/dev/sdc26	8118272	8736767	309248	a8	Darwin UFS	CACHE	cache.img.ext4
/dev/sdc27	8740864	9005055	132096	a9	NetBSD	TOMBSTONES	tomb.img.ext4
/dev/sdc28	9011200	10035199	512000	95	Unknown	HIDDEN	hidden.img.ext4
/dev/sdc29	10035200	30777343	10371072	90	Unknown	UMS	ums.rfs