SQL Server Backup To a NAS Box
It means either it's permission issue or you are running out of space on target.

Permission Issue

The service account of SQL Server (which used to start SQL Server service) does not have access to the target.

START > RUN > type SERVICES.MSC.

Find SQL Server Service > Right click and go to PROPERTIES.

Go to LogOn/Security tab

If it's system account (NETWORK SERVICE, LOCAL SYSTEM etc.) then change it to any specific account (domain account like ex. dba\sqlserviceact).

Then restart SQL Server Service.

And grant the account (ex. dba\sqlserviceact) read &amp; write privilege on the shared folder (network path).

If it's other then system account the grant the account ready/write privilege.

Thanks