So, my phone has died twice in two days. I have to take the battery out to be able to turn it on.
I can swap the phone for the a brande new one, but only until tomorrow. Should I do this? Will the deaths become more frequent?
The only reason I don't want to swap it, is because I have it running exactly the way I want it, and have all my apps that I want on it.

If its rooted use Titanium Backup to back everything up then when you get a new handset just re-install titanium and restore your settings and apps :)

If its not rooted might I suggest going to appbrain.com and using their free service, sync your apps to their site then at least you've got a list of apps for when you get your new handset :)

well it happened to me too on the stock firmware that came with the phone, but was completely GONE when I flashed the phone to a newer firmware (such as JG5 or M5) which concludes that the problem was caused by the stock firmware as it was buggy (it was lagging and freezing on me sometimes)

I suggest that you back up your phone as JSG10 mentioned and then flash it to a newer firmware to see if the problem persists (you might void your warranty if you flashed your phone)

hope this helps you...