Computer needs to be powered on after being put in sleep mode

Hi everyone,

Recently (for about the last two months), whenever I close the lid of my computer and put into sleep mode, I have to plug it in and press the power button for it to start again instead of just opening the lid. I went to Genius Bar once last month because the computer was unresponsive and they said it could be a battery issue, even though the battery diagnostic test passed. The battery is at ~1300 cycles and I was wondering if replacing it could solve the problem. Any thoughts?

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Late 2011 13" MBP 2.5 GHz i5 500 GB HDD 8 GB RAM