was having the same problem... here's my sequence of events
1. bought sgs3 with ICS and installed foxfi, worked great with no issues.
2. vzw updated sgs3 OTA to JB and broke foxfi, tried other tethering apps (Fattin toggle, pdanet etc) nothing worked.
3. did a factory restore, which fixed tethering for a few hours but then the data started dropping again, started getting really frustrated and considered rooting and reinstalling ICS
4. tried changing the name of the hotspot and that seemed to fix Fattin and it has been working fine for about 3 days now