WiFi was connected throughout (until disabled) and with the phone left on the kitchen counter unused. Signal was adequate if not strong, and ought not to have led to signal dropouts. The drain rate with WiFI on was 5% per hour with the phone idle, suggesting a flat battery from an unused phone in just 20 hours. I don't recall exactly how things faired with ICS, but I'm sure they were MUCH better than this.
FWIW I've been running JB for a couple of months (original German JB ROM and now the latest German ROM) and the issue is/was present on both ROMS.