iPhone shuts down randomly

Hi,

my iPhone shuts down itself completly random. But i can't figure out WHY it does. Im quite sure that it is a shoutdown because I saw the animated circle for about 20 seconds before the screen turns black.
Sometimes it shuts down twice a day, sometimes it runs perfectly for many days without any error.

First I tought it's a problem with my handy-bag: It's filled with nylon and so I thought, that there could be a problem with electrostatic charge. But I carried around my iPhone in a normal cotton-bag and it shut down again.
My current impression is, that there is a problem with (dis-)connecting the headphones or the iPod-App itself. I came to that thought, because in the time I didn't use the iPod, the iPhone didn't shut down.

I tried a reboot, hard shutdown, reinstall firmware with and without backup.

Any suggentions?

Thanks for your help in advance!

Phil