Okay. I figured it out. It will redial, but you have to hold the button in until a second short beep is heard. I wasn't holding it down long enough.
It is actually in the manual,
but it is hidden under a heading of "Once you're done pairing, the following new headset features will be available:"
The first bullet is:
"Last number redial (when not in a call)
While the headset is on, press and hold <phone button> until 2 short beeps, release immediately."
Actually now that I'm really looking at the manual I see the stuff I quoted before is under step "13) Enhanced features (for Bluetooth phones with hands-free profiles)," and then goes on to list a few Nokia models, Sony Ericsson, and Siemens. I assumed the BlackBerry wasn't one of them and skipped the entire section. I would be that is a common mistake.