My bose headphones keep turning on and off by itself when the battery has only been used for less than a week.

Those are usually hermetically sealed. You will damage the housing if you try to replace it..

Either the batteries are used up an cannot be charged any longer or the charger is broken.

Choose another app.

Mine did this as well, totally frustrated I kept on rapidly switching them on and off, and eventually it just switched on!

Mine do the same thing when the battery is nearly dead. Have you tried changing the battery?

Time to replace the battery.

The exact same thing happened to me, and I was using the same brand of headphones. :/ At first I thought it was just a **** brand, when my left headphone stopped working and sound would only reach it if I adjusted the base of the headphones - the bit that connects them to the iPod - a tiny fraction. I had to keep adjusting it to get it to work.
But it turned out that this is a problem that occurs in all brands of headphones. I went from Skull Candy to Sennheiser to Apple to Skull Candy again to Bose and no matter what brand it is, it will happen eventually. I don't think there is a solution, except to keep buying new ones and try taking them out of the iPod more gently and less frequently.

I've noticed a second or two of silence when bumping the headphone. In my case the battery was low and a fresh battery fixed this particular problem. Or maybe you have a poor connection.

same thing has happend to me, sometimes when im playing around with it i get about 2 hours use before it turns off again. do you recon its worth sending it off to bose for repair?

Yeah, based on all of your problems, i would safely say that you have a blown speaker. Call up Bose at 1-800-999-2673. If the headphones are under warranty (1 year) they will replace them for free. If now, they will charge you $100 for a replacement pair, which is quite a deal considering that the headphones cost $300.