To answer your question, rather than pointlessly ask for system specs which is still an annoying hazing ritual on this forum, the answer to your question is that it is completely abnormal for Vegas to hang when you switch to another application during render.
The reason that system specs are pointless to ask for is that unless you had some sort of pathological system build (e.g., only 500 MB of memory), nothing in the very short list of information in the "system specs" will provide any information whatsoever that has anything to do with your problem.
Crashes sometimes have to do with overheating. You can download one of several free utilities that will tell you how close you CPU might be to overheating.
Crashes can also be caused by misbehaving applications and background processes.
If you are using the GPU during render, it is possible that might be causing a problem. Again, system specs don't require that you provide information on the specific driver version that you are using with your graphic card, but that might be the cause of the problem. This is easy to test: turn off the GPU and try rendering again.
Grazie asks some good questions. Another one that is critical to answering your question -- and which is totally absent from the absurdly unimportant "system specs" -- is which version of Vegas you are using? Vegas has developed stability problems ever since version 8.1, but they are different from one version to the next. A very relevant question is to ask which version you are using (10, 11, 12) and which release within that version (consult the Help --> About dialog). Some of the releases of each version were unusually unstable, and you might get some relief by updating to the last version within whatever release you are using.
I thought I remembered this . . . Back in August one of chums here had a "Render As Issue", with a Catalyst card, which I read in your System Specs. Could be another glitch emerging for you too, combined with the stability issues over the past Builds - dunno. http://www.sonycreativesoftware.com/forums/ShowMessage.asp?ForumID=4&MessageID=868454"In the end we unistalled the ATI catalyst graphics card driver."[/link]
No matter what you're doing, switching to a browser shouldn't freeze anything, unless there's a very specific reason (IE you are using a full screen program and it doesn't like not being in front).
If you switch to an explore window, another instance of Vegas, etc. does it freeze? What about bringing up the task manager? What about IE? Yes, it's a browser, but it's part of Windows so trying to narrow down what it could be.
Are you always rendering to the same codec? does it REALLY hang or everything just takes forever to get responsive again?
Keep in mind that the browser is a huge memory hog, especially Chrome. It could be simply that Vegas isn't "hung", but just waiting for some RAM to be free, or worse swapping into Pagefile which can appear to be "hung" because hard disk as RAM is painfully slow.
There's no way the computer should pause for more then a second or two on anyone's rig who's using Vegas when switching to a browser. Not under normal circumstances. I can get several second pauses with two instances of Vegas open, each running on two cores, and Blender rendering, then switching to Firefox with ~a dozen or so tabs open.