In windows, drive mappings are on a user account basis. This means that the user account that the SQL Agent runs under can't see drive mappings made by a different user (like the account used to administer the server).
A workaround is to use a UNC path name to point to the share. Just type in whatever file path you like into the "Output File:" field in the Job Step Properties dialog box. You might want to dream up some sort of naming convention to keep server names, job names and steps straight. Something like:
\superbigfileserver\sqllogshare\sqlagentlogs\dbinstancename\a_sql_job_name.step_number.txt
Of course, the account used for SQL Agent should have sufficient permissions to access the relevant share, path and file.
If you are worried about the name of the file server changing, set up a CNAME via DNS and use that name instead of the "real" file server name.