Typical symptoms of failure can include misfiring and stalling, high surging idle and poor fuel mileage, but of course these can also be caused by other issues. Usually a trouble code will be set during failure, causing the "check engine" light to come on.
If you're troubleshooting a driveability issue, always start by checking and diagnosing the trouble codes.
"The BAP sensor measures barometric pressure using a frequency. This gives the PCM (computer) information on engine load. It is used as a barometric sensor for altitude compensation, updating the PCM during key-on engine-off and wide open throttle (WOT) events. The PCM uses BAP for spark advance, EGR flow (if so equipped), and air/fuel ratio."