@Uzair Mehmood Pasha Thanks for asking question! You may want to know that-
429 error occurs when you have too many deployments/failed deployments of an app service plan within a short period of time. This causes the system to throttle any additional deployments for the next 48 hours. This limit is per region, which is why you were able to use other regions or subscriptions.
If this occurs, you will need to wait 48 hours to complete a deployment in that region or contact support to see if they will remove the throttle.
Also, App Service Plans have a 10 per region limit on the Free SKU and 10 per resource group on Shared SKU and further limits according to SKU is listed here.
Depending on your plans you would need to either move to higher plan, or raise a support ticket to see if the limit can be raised you may also want to check the other limits in that link. In case you don't feel you are hitting any limit then you would need to raise a support case.
Further you may refer to similar queries here would be helpful.
Please let us know if issue remains, happy to assist you further.