Debian Hardware :: Reinstall Broadcom-sta-dkms On Every Boot

About 6 months ago or so, I got a new 802.11ac card for my laptop:

$ lspci | grep Broadcom
07:00.0 Network controller: Broadcom Corporation BCM4352 802.11ac Wireless Network Adapter (rev 03)

This one uses the broadcom-sta-dkms binary driver in module wl. Everything was working fine until a few days ago. I booted up the laptop following a power failure and the network was acting very strange. Upon connection to the network, I had network access for a brief period, then it went away. Network manager claimed to still be connected. The access point thought I was connected as well. No packets were getting through. After many cycles of trial and error, I found that upon each network connection (different network, same network, didn't matter) I could ping the router for about 30 - 45 seconds.

After that, my pings went unanswered. Using wireshark in monitor/promiscuous mode, I found that I was indeed not seeing any replies and no machine on the network was responding to my ARP requests. Inspecting the ARP cache before and after, I see the mac address of the router as usual up until a couple of minutes after the pings stop coming back. I am also seeing wireless activity from other machines on the network, but I think it was only broadcast activity I was seeing. This behavior didn't change with signal strength either. I saw the same behavior when I was 3 feet from the router as when I was 50 feet from the router. Wireshark didn't show any other activity that looked out of place to me.

I did find a work around. If I purge the broadcom-sta-dkms package (apt-get purge broadcom*), reboot (haven't checked if unloading the wl module is sufficient), install the broadcom-sta-dkms package, and manually load the wl module, everything works as expected. I'm not sure why the driver won't survive the reboot. I have had to do this each time I boot my laptop for the last few days. I'm not sure what might have changed as before that power failure I think I had a couple of weeks uptime and I do updates at least weekly. I think I remember seeing an update to the kernel come through at one point recently. I tried reverting to the previous kernel version but that didn't seem to do the trick.

I'm on Debian Jessie.