Not sure if this will help anyone, but it seems to have fixed the problems I've been having the last few days. Xbox Live has been disconnecting frequently and sometimes not connecting at all. Troubleshooting indicated that this was not an ISP or router issue.
Anyway, I was testing my network on the Xbox to little success (couldn't connect to Live). I noticed that there was an option to manually configure the network. I choose to change the DNS settings from Automatic to Manual. Research online led me to use 188.8.131.52 as my Primary/Preferred DNS address. I made the change, tested again, and huzzah! Success! Everything seems to work as it did prior to the recent system update.
Anyway, it's worth a shot for some of you having the same problem with inconsistent Xbox Live service.