Your bike has a DC powered CDI, any battery problems will have it doing what you found. The battery is failing or you have a load that is running it down. Check for damaged/pinched wires everywhere. Cut open the loom if it has worm spots. A shorted out wire should be visible due to arcing.
You may have to disconnect every single connector and put it back together one piece at a time while using a multimeter to check for current draw.
A broken wire can have similar results if it stops the CDI from getting power. Charge the battery and hook it up to different bike. See if it can crank the engine without losing cranking speed (a poor man's load test).
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2011 EC250E
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