As a random guess (I can't see the code in your bat file), it is either using relative paths OR is using network shared drives.
Since SQL says it ran successfully, it is VERY likely that it ran to completion. What you could do is add some logging into your bat file so you can tell what has been run and were it ran into problems. Inside your bat file, you can redirect all errors to a file and all output to a file. This will help you in debugging what went wrong.
Another possible problem could be permissions as that bat file is being run as the SQL Server Agent Service account, not as you. So running the bat file as yourself doesn't really tell you anything that useful.
An alternate way to run it where you can have more control over who is running it would e to use windows task scheduler. Depending on your needs, this may or may not work for you.
The above is all just my opinion on what you should do.
As with all advice you find on a random internet forum - you shouldn't blindly follow it. Always test on a test server to see if there is negative side effects before making changes to live!