Is it the phone VLAN in this one area that fails, or the entire voice VLAN (assuming it is one broadcast domain)?
I would be looking at switch logs... and no, I don't believe the 3300 can help you diagnose this. If you know it is a specific area then the switch for that area would be the logical one to be examining the logs. Usually the only way a broadcast storm can occur from a phone is if the PC port is looped back into a wall jack, but spanning tree should shutdown that port, not the VLAN at the uplink level. How many phones in this area? Can you eyeball each one and see if someone looped a cable to a wall jack or mini switch?