Did you upgrade from another Palm device? If so then I'd suggest deleting the Saved_Preference.prc file from the device - you'll have to use a secondary program such as FileZ to do so. It's available at www.palmgear.com as freeware.
You will lose any saved preferences and it will cause the device to look like it underwent a hard reset but your data will still be intact but passwords and registration numbers will have to be reinputted for any software.
Also, if you upgraded from something else it could be a software conflict.
Also, did you apply the SD card updater to the device from PalmOne located here
I'd suggest apply my suggestions in reverse order.....go to the PalmOne site first and apply the patches that are on that page then if that doesn't work delete the saved preferences.
The SD patch fixed several issues and just because your T3 is new doesn't necessarily indicate that it would have been applied before your purchase.
You can try a little experiment - remove the SD card (if there is one in it) and see if you get the soft resets you describe. If no then it's the patch is needed if yes - then it's probably software related.