From the error messages provided, seems like the server load was too high to create a worker thread. Please check the following and proceed accordingly.

>> Try to run the FULL backup in non peak hours and check if this works.

>> While the backup is running, check to see if they are any parallel high resource intensity jobs\process is running, which is causing this error.

>> This can also be because of the huge concurrently active user connections on the server.

>> Also it could be because of the virtual memory issues. SQL Server may generate these kind of error messages after the whole virtual address space is used up.

Check if the server is facing any of the above situation.

-Rajini