You may have the Action Rule set to "Delete file from (local folder) After Transfer" for the condition when you "Transfer file from (local folder) To (remote folder)". Check the Action Rule you have set for Local and Remote folder synchronization. You can change the Action Rules by right clicking the profile that you are synchronizing and selecting Edit Profile]Transfer tab]Action Rules. For more information on Action rules, you may visit the help page on Action Rules

Auto FTP manager compares files present on the local and remote end by name, size and date. Synchronization is done by comparing the remote and local folder contents to determine which files need upload or download. For more on Synchronization in Auto FTP manager, you can also visit the following page: https://www.deskshare.com/help/afm/ActionRules.aspx