[Verizon Samsung Galaxy S III] BitMaster:
I've had the same issue with 4G data dropping using the hotspot and it appears worse since the JB update on my Verizon S3. Interesting enough, I have no issues using the tethering option via Bluetooth.

Note my phone is stock, not rooted.

FoxFi used to help (I'm paying for unlimited tethering) but since the JB update it doesn't matter. In fact, when I reinstalled FoxFi and turned on the hotspot via the app, the Verizon hotspot app also starts. This never happened before but appears to have happened since the JB upgrade.

I read in another forum to try turning off WPA2-PSK security all together and turn on Open. I've just tested that and it appears to not kill the 4G connection. I did turn on only connect to allowed devices... It's easy to add them by turning that option off with just "open", then add the device(s) by selecting the "+" to the right of the device so they are then listed in the "approved" section. Then turn back on "only allowed devices".

I have not tested the WPA-PSK encryption to see if it drops (yet).

I don't particularly care to run an open network with no encryption as any packet sniffer can pick up plain text (although browser encryption keeps secure sites secure) and allowing only certain devices works off the MAC address, so it's "relatively" secure. And by relatively I mean not greatly secure because a techhead can spoof their MAC address. But since it's a phone, my hotspot isn't always on...

I also need to test running a tablet along with my PC to see if the 4G drops or not.

Some other notes with the problems I'm having:

- The phone doesn't drop signal. Test programs show the signal connection constant. The mobile data simply turns off on the phone and pops off and on,,,

- I had this same issue with my HTC Thunderbolt.This leads me to believe it's a Verizon problem, but since the open option is appearing to work, that doesn't seem 100% true.

- Bluetooth tethering is fairly solid. Minimal drops, but Bluetooth doesn't appear to be quite as good as passing data as WiFi.I don't have bandwidth specs handy

- Since going to open/limited approved devices I'm streaming video in the background on Chrome browser and also surfing XDA at the same time with (fingers crossed) no 4G drop,

- After changing to open on the hotspot, I did shutdown and reboot the phone.

Let me know if this helps your situation.

UPDATE: Well after all that, I added my Nexus 7 to the hotspot and within seconds it dropped 4G data. Now it's dropping periodically even with the Nexus off and just the PC connected. So I dropped it back to completely open not limiting devices and it appears to be not dropping. Buggy PITA!

UPDATE #2: Just got off the phone with Verizon Tech Support. This is apparently a known problem with ICS on this device and they are working on an update. They offered me a replacement phone but I bought this new and do not want a refurb, so I declined. They then suggested a SIM card replacement as this is where all the info is used for security to/from the network and if the SIM card does not fully fix, then a factory reset and reinstall of all programs (which I knew was coming).

---------- Post added at 09:02 PM ---------- Previous post was at 08:43 PM ----------

With my experience, if you update to JB you will experience the drops. I didn't have as much of a problem with this with ICS.