I used to have a cingular prepaid phone. It liked to shut itself off when I hadn't used it for a couple days. Fine, right? Saves batteries? Except the dingdangity thing wouldn't turn itself on again if I got a phone call! 
That was the most useless 'feature'! So giving out that number wouldn't have helped anyone get in touch w/ me.
If your phone was shutting itself off, it was probably doing so because the battery got low. That's the only time I've had a phone actually shut itself off. (Either that, or you have it unlocked in a purse or pocket and it's getting banged around and the power button gets hit -- I've done that.)
Well, I had a spare charger that I kept plugged in at work, so the phone was charged 2-3 times per week, all day. And it was one of the folding types, that I carried in a case, so it shouldn't have had any buttons bumped. And really, if the phone decides to shut
itself off, instead of me doing it, I'd really expect it to wake up when a call comes in. Like how my camera goes to sleep if I leave it on but don't use it for 5 minutes or so. But when I touch the shutter, it wakes up.
When I used it, it would stay awake for a few days. Then it would decide it wasn't needed, and would go to sleep. I found this out when I was in NY for the day, and expecting my family to call and arrange to meet up. I thought it odd that I didn't hear from them. When I finally called, they said they'd been trying to call all day and getting a message about me being unavailable or something.
The phone was a piece of junk, basically. I don't use the current one much more often, but it stays at the ready in case I get a call. Which is what I;d expect it to do.
