AVR-Chat

So I'm looking at deploying a device with a Li-Poly battery on board.  
The voltage of a fully charged battery should be 4.2V, and will drop 
over time.  My application calls for a 3.3V source, and I was looking at 
using a LDO voltage regulator which has a *fault line to indicate when 
the voltage out is not correct (i.e. below 3.3v).  At this point, I 
would like to shut down the device, but I'm not sure how to do it.  If 
the device shuts down, I expect the voltage to rise above 3.3v, the 
device will power on again, the voltage will drop, it will shut down 
again.... et cetera... and just oscillate using up more battery and 
possibly permanently damaging it. 

This would seem like a common problem.  Has anyone else run into it -- 
and if so -- what solutions are available?  I can shut down a lot of the 
peripherals on the board, but there will be a number of components that 
I can't shut off and I don't want to run into the situation where the 
battery is bled dry.

Thanks in advance!
Reza