I don't think that deleting the apps alone will resolve the problem. You are probably going to have to perform a Factory Data Reset. Something seems to remain when apps are deleted with Android, at least that has been my experience.
A computer (and make no mistake, this phone is a computer) shuts down on its own for only a couple reasons. It runs out of memory, or its CPU (processor) becomes overloaded. In the case of these phones, I believe that it may be the latter. A rogue application begins eating processor cycles and finally the phone can't take anymore, throws up its hands, and shuts down.
A Factory Data Reset is really not all that hard to perform. You'll want to make certain that all of your contacts are backed up, either through GMAIL or My Contacts Backup. You will need your GMAIL account info (email address and password), plus account info for any other email addresses you have on the phone. You may want to list out the applications you've installed. I did this using the text editor on my computer.
Your data (media files and documents) is not stored on the phone itself. It is stored on the memory card, which is not touched during a factory reset.
Once this is accomplished, you will go to Settings > Privacy and tap on Factory Data Reset. You will be queued twice on "do you really want to do this" and then the phone will be wiped and reset to default settings. The phone's basic programming will not be messed with.
Once the phone comes back up, log into your GMAIL account, using the GMAIL application (white envelope, big red "M"). Next, recover your contacts, either through logging into your GMAIL account or through running My Contacts Backup. If you forgot your MCB password, there is a link at
http://mycontactsbackup.uscellular.com to send it to your phone in a text message. After logging into GMAIL and getting your contacts back, I generally direct folks to a few settings that will help your GPS to function better. The can be found under Location & Security, Accounts & Sync, and Privacy, under Settings. Under the first two, make sure the top two boxes are checked, and under Privacy, make sure Use My Location is also checked. Next, go to your browser, navigate to
Google, and there tap on Settings. Scroll to the bottom of the resulting page and tap on the "Yes" radio button for "Allow use of device location?" Select Save and you will be returned to the Google page. Tap on your Home key to get back to your main screen.
Next, set up any other mail accounts. If you are setting up a Yahoo account (this includes AT&T Yahoo variants) I strongly recommend using the Yahoo Mail application found in the Android Market instead of the phone's Email applet. I also recommend using the Hot Email app for Hotmail accounts.
Finally, take it easy with the third party apps.