Do you mean turn off completely where you have to power it up again? Or you could've mistaken the auto screen off as being 'Off'.
Or simply the obvious....fully charge your battery to full capacity before using your new phone. If all else fails you could have a faulty battery form the start ( which is very rare) Good luck!
you'll need to elaborate.. in order to save battery the screen will automatically dim and then turn off every 30 seconds, you can set this to 30, 1 min, or 2 mins. I use 30 seconds as I'm fine with "waking" up the screen when needed.
There is actually an issue with the Incredible in NC for some reason... Verizon suspects it has something to do with cell tower hand-off in low signal areas.
Read the Engadget article: http://www.engadget.com/2010/05/01/htc-incredible-suffering-random-reboots-for-tar-heel-fans-and-du/