@ravideva-7719
Based on case verbatim we understood you are trying to export the database with network restrictions in storage account.
We checked the previous issues raised with similar error and found this is not supported and we need to enable all networks in storage account to be able to export the Azure SQL database. This happens as IP address for Azure SQL is dynamic.
There are list of IP ranges for Azure SQL databases but adding them to the network list will not be helpful as Database Export/Import operations will occur on the back end and it uses other Azure SQL services in the back end to process these requests. Hence only option here is to allow all networks in storage account firewalls. Apologize for the inconvenience but unfortunately that is by design limitation for now.
Please try and if successful also post your feedback here - https://feedback.azure.com/forums/217298-storage as storage team will be able to see this and take action.
Regards
Navtej S