Repeated flats, yet no puncture. A puzzler.

[elocs]

My 19 year old goddaughter has a cheap Walmart bike, fat tires. A few weeks back she got a flat in the rear tire with the brake pads totally locked onto the rim to where the wheel would not even move and the inner tube coming out of the tire.

I no bike mechanic, but I have changed bike tires for 50 years now and so I thought it wouldn't be a problem. There were no loose spokes so I just got a new tube and it was fine. Until a few days later, then flat again.

This time upon checking in the tried and true manner of holding the tube in a sink full of water I found a puncture. This time I got a self sealing inner tube and it was fine.

Now the rear tire has gone flat again. First it took a day to loose all the air, then a matter of minutes upon riding. I just got the tube off and checked--no sign of a puncture (but it is a self sealing tube and I've never used one before). I can see nothing on the tire or rim that could have caused the leak and again, the spokes are all tight.

What could be causing this tire to totally lose its air within minutes of riding when there is no apparent puncture? Does it need a new tire?

I'm flummoxed so any help is appreciated.