Cloudformation , AWS::ApiGateway::Deployment not update Api deployment

AWS::ApiGateway::Deployment will no update

Recently, we use AWS cloudformation to deploy our api gateway,

we use AWS::Serverless::Function, and AWS::Serverless::Api to deploy our beta stage, it works, and use AWS::ApiGateway::Deployment to prod stage, it only works on first time, and will no update when we deploy agin :(

our template like this:

sam_template_beta.yml //for deploy beta, it will update every time when I deploy

#sam_template_beta.yml
AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Description: api sample
Resources:
  lambdaFunction:
    Type: 'AWS::Serverless::Function'
    Properties:
      FunctionName: lambdaFunction
      AutoPublishAlias: beta
      Handler: lambdaFunction.handler
      Runtime: nodejs6.10
      CodeUri: .
      Description: test api
      MemorySize: 128
      Timeout: 3
      Role: '$lambdaRole'
      Events:
        Api:
          Type: Api
          Properties:
            Path: '/v1/test'
            Method: GET
            RestApiId: !Ref apiGatewayLogicalName
  apiGatewayLogicalName:
    Type: AWS::Serverless::Api
    Properties:
      DefinitionUri: ./swagger.json
      StageName: beta
      Variables:
        env: beta
Outputs:
  apiGatewayLogicalNameRestApiId:
    Description: ""
    Value: !Ref apiGatewayLogicalName
    Export:
      Name: apiGatewayLogicalNameRestApiId

sam_template_prod.yml //it only works on first deploy, and not update prod stage next time :(

#sam_template_prod.yml
AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Description: api sample
Resources:
  apiGatewayProdStage:
    Type: "AWS::ApiGateway::Deployment"
    Properties:
      RestApiId: !ImportValue apiGatewayLogicalNameRestApiId
      Description: "prod"
      StageName: "prod"

we found, when logical name change, it will deploy stage :), show we change sam_template_prod.yml content

#sam_template_prod.yml
AWSTemplateFormatVersion: '2010-09-09'
Transform: AWS::Serverless-2016-10-31
Description: api sample
Resources:
  apiGatewayProdStage$timestamp: #original apiGatewayProdStage
    Type: "AWS::ApiGateway::Deployment"
    Properties:
      RestApiId: !ImportValue apiGatewayLogicalNameRestApiId
      Description: "prod"
      StageName: "prod"

great :)

hope this one can help who has AWS::ApiGateway::Deployment can not update issue