It was back at the dealer after only a month. It always starts the first time, but any time after that will not start with the electric starter. My dealer tells me this is a "trait" of the Kymco Agility; it needs a little gas on the throttle once the engine has warmed up and been turned off. It has been to the dealer three times for the same problem. They have now told me I need to deal with this quirk, because they took out and replaced every part, and it still has trouble starting once the engine is warm.
Unless it has warmed up for 10-15 minutes the first time it's started that day, it is sluggish taking off. Once the engine has warmed up, the problem goes away.
This may not be everyone's problem, but where I live there aren't many Kymco dealers. It's a hassle to find someone who will fix it under warranty. I'm hoping I don't have any more serious problems with it in the future. I will probably sell it before the warranty is used up.