Having a similar issue, but with a much larger net. I used transfer learning to make a custom version of VGG-19/ImageNet. It works fine locally. CloudDeploy took about an hour and ballooned memory to something like 24GB! It finally finished, without an error, but trying to load the URL produces {"errorCode":"no-wolfram-engine-response","statusCode":503,"errorDetails":"Unable to evaluate"} The upload code in question is

link = URLShorten[
  CloudDeploy[
   FormFunction[{"photo" -> "Image"}, 
    vggNetClassifier[#photo, "TopProbabilities" -> 2] &], 
   Permissions -> "Public"]]

Is it just too big a function to deploy? I hope not if Wolfram is serious about making deep learning easy to use and deploy...