The "Bank Angle Sensor" is part of the TSM/TSSM (turn signal/security module), and is designed to shut the engine off if you exceed a 45 degree bank angle for more than one second. When the sensor kills the engine, the odometer will display "tip". To restart the engine, make sure it is upright and then cycle the ignition switch off then back on.
There were problems back in '99 or '00 if I remember correctly with defective sensors that would shut the bike down during normal operation (shiny side up), but I haven't heard of that issue since then. In this case, I seriously doubt that the bank angle sensor has anything to do with the stumble/stall problem. So far, everyone has indicated that the "hiccup, stumble, stall, etc." is only a major issue before the bike reaches normal operating temperature. This makes me believe that it is a too lean mixture and poor atomization of the fuel when cold. H-D has their ECM's programmed to come out of cold start/warm up enrichment way too fast, to more easily meet EPA emissions standards. If you have a SERT, you should be able to change the values in the "cold start" and "warm up" tables to richen the mixture until the bike is actually warmed up. One of the SERT experts on this site could probably give you more detailed information on accessing the tables and recommended settings. For those with other tuning devices like the PC, you have to richen the low speed mixture (1000 - 2000 rpm @ 0 - 10% throttle) just enough to eliminate the stumble when cold without going too rich when up to normal operating temp. That's the method I used, since I don't have a SERT. Once you get the low speed mixture dialed in, you'll also notice that the bike will run smoothly below 2000 rpm. Stock, it bucks and jerks any time you let the rpm's drop below about 1900.
Jerry