Also, there is a reset pin...better make sure that you don't need an external pullup on this..bad things happen when resets float ya know.  I don't have the data sheet handy, but im sure the spec is there.
   
  If indeed....it really is in a cyclic sleep mode, then I do agree...look at battery technologies that might be better suited.  Use a LiON battery with a boost to keep the voltage up at 3V even when the input is lower.

       
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