First off, check the connectivity path you are using: are you connecting via the latest documented method? Cloud SQL used to have a connectivity path which is slower and is now deprecated, but still functioning, so you could be accessing via that.
Second, is the App Engine app and Cloud SQL instance in the same location? Check that the "Preferred Location" in your Cloud SQL settings are set to follow the app engine app you are connecting to.
As a last possibility, which seems unlikely given that you have data connecting locally, make sure you are reusing database connections, making new ones can be expensive. If there was some reason why your app is reusing connections locally but making new ones on the App Engine side, that could create this behavior. But like I said, this one seems unlikely.