It sounds like you need to find the actual error that you're experiencing, the 503 isn't enough information. Can you provide some other context?
I'm not familiar with fargate but have been using ecs quite a bit this year and I generally would find that by going to (on the dashboard) ecs -> cluster -> service -> events. The events tab gives more specific errors as to what is happening.
My ecs deployment problems are generally summarized into
- the container is not exposing the same port as is in the definition, this could be the case if you're deploying from a stack written by someone else.
- the task definition memory/cpu restrictions don't grant enough space for the application and it has trouble placing (probably a problem with ecs more than fargate but you never know.)
- Your timeout in the task definition is not set to 8 minutes: see this question, it has a lot of this covered
- Your start command in the task definition does not work as expected with the container you're trying to deploy
If it is pulling from docker hub continuously my bet would be that it's 1, 3 or 4, and it's attempting to pull the image over and over again.