Hi, you are definitely experiencing OS errors.
From the error below, you could be experiencing some disk problems, the write process does not get to complete writing consistently to the disk.
Application popup: Windows - Delayed Write Failed : Windows was unable to save all the data for the file D:\[FILENAME].zip. The data has been lost. This error may be caused by a failure of your computer hardware or network connection. Please try to save this file elsewhere. "
So I have a question: do you have some other disk that you can backup to other than drive D?
I suggest that you check drive D for sector failures. if you're working off a drive which resides on a centralised storage system then get to fix your connectivity errors with your storage experts.
For a start, try backing up to a different drive other than D drive and after a successful backup then you may have to shut down SQL server and any applications which might be accessing D drive on your system, then run a CHKDSK on your D drive.
If you have any disk errors then get them fixed. This will solve your file writing issues.
You will have to check how consistent your database is using DBCC CHECKDB before backing up to ensure that you backup consistent data.
Regards,
Chris.