The EDI Server runs as part of Microsoft Internet Information Services (IIS). For security reasons, IIS runs under a special account that can read and write to only a small number of directories. (This is so that if the IIS server is compromised, the damage can be contained.) It is likely that this account does not have permission to write to the directory you specified.
Configure the directory permissions for the directory that you want the logging output to be written to, so that the IIS account has permission to read and write to it. The exact account used by IIS depends on its version and protection level. The simplest solution is to allow permissions for all three of the possible accounts, as follows: