My first thought is that the battery is loose - and if it's a loose battery connection, you can try using a piece of an index card in the battery case to make a tighter fit (we did this with my daughter's Env3; it did work).
If that ISN'T why it's turning itself off and on, then getting to the root of why that's happening would be the route to a solution. Does it happen randomly? Or is there a pattern? Is it in a pocket or sitting on a table when it shuts off? In the middle of texting? Calls? Sorry for all the questions, but it may help narrow down what the issue is.