This may occur even if Attunity Replicate is working fine. To fix it, run below statement:
USE <the database name that's in the error> GO EXEC sp_changedbowner '<the user which has sysadmin privilege>' GO
for example:
USE databasename GO EXEC sp_changedbowner 'sa' GO
What this does is it changes the user mapping within the login properties of the stated user. You should no longer see the error within SQL server error log.