So, I'm by no means a linux expert, have no idea what half the daemons are doing in the background, but I'm reasonably intelligent and wasted most of my morning trying to fix my own (recently upgraded) installation of Ubuntu 12.04 and THINK that I've got a fix, although somebody who knows what he/she is talking about might better explain what it is that this "fixes". Over the past couple days, I noticed the same bizarre spotty network access and assumed it had to do with either Comcast sucking or my internet being throttled, neither of which wound up being the case after talking to customer service. Anyhow, after much wasted time, and observing that my connection wasn't actually dropping, as once I started downloading the ISO for Ubuntu 12.04 (was pretty close to just bailing and reinstalling from scratch), the connection and speed were fine. This got me wondering if the issue was DNS. If you start Googling that, I think other folks are having similar issues...
Anyhow, long story short, I think the issue is something called "dnsmasq", which apparently is new to 12.04. There's some discussion of it here, although I'm still not sure I really understand what it's doing:
If you disable this as described in that link, ie:
sudo nano /etc/NetworkManager/NetworkManager.conf
Comment the line:
Save (Ctrl-O). Close (Ctrl-X).
sudo restart network-manager
After doing that, Chromium is happy again. Again, I should warn you that I don't really understand what the implication of disabling "dnsmasq" is, but maybe some moderator or administrator can see whether that shines any light on the issue? Hopefully this resolves your problem as it did mine.