There is a known issue with Fedora 15+ and BCM4311 wireless cards where the wireless will connect, stay connected for a few minutes, then disconnect until either the machine is rebooted or wpa_supplicant and NetworkManager are rebooted. The latter does not always solve the problem. I've personally observed this issue being more prominent when large file transfers are taking place.
Before taking these steps you should verify that you do indeed have a Broadcom BCM4311 wireless card. This can be done with the following command:
lspci | grep -i bcm4311
You should see something along the following if you have the card:
0c:00.0 Network controller: Broadcom Corporation BCM4311 802.11b/g WLAN (rev 01)
Ensure you have a wired connection as you will lose access to the wireless card during this process. You have been warned :). Please also note that the following commands (with the exception of the reboots) won't do anything unless you have the RPMFusion repository installed.
As root install the akmod-wl package and reboot like so:
yum install akmod-wl -y reboot
Once the system has finished rebooting, perform a system update which will grab a few additional packages, and reboot once again:
yum update -y reboot
If you are unable to see the wireless card then this solution probably hasn't worked for you. You can bring the card back online by running the following as root: