The SSM API in general has a low throttle limit. When we first implemented SSM, I hit the throttle limit while deploying a CloudFormation template that invoked 4 nested templates in parallel, each attempting to deploy 15 parameters. Eventually got it working by explicitly setting dependencies in the template so CloudFormation was forced to deploy the parameters in serial.
I can also vouch for the need to cache the retrieved values in the Lambda container to avoid hitting throttle limits at retrieval time.
we recently hit the cloudformation limit too and add to start using the nested templates.. it was a "nice" surprise when we could not deployed for the 200 resources limit error. i will probably write something about that too :-)
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