I know it sounds like we're talking in a circle here, but one more time for clarity:
Yes, it is possible to give people rights to do just about everything but delete a file. No, it is not practical or recommended to do so, especially for a file server/shared files.
Applications are written to assume that certain basic permissions are being used, those are usually Read, Write, Change, and Full Control (which is everything). Beneath that you can get more granular, down to Traverse Folder/Execute File, List Folder/Read Data, Read Attributes, Read Extended Attributes, Create Files/Write Data, Create Folders/Append Data, Write Attributes, Write Extended Attributes, Delete, Read Permissions, Change Permissions, and Take Ownership. These more granular components are the "building blocks" that are used to create the higher-level file permissions. If you grant users permissions at the most granular level, then applications may assume that they have the entire set of permissions for that higher-level permission, which could cause issues or unusual behavior.
So basically, don't do it. Give people read/write access to the files that they need to be able to read/write to, give them read access to the files that they need to read, and make sure that they have no access to files that they don't need. Don't worry about trying to keep people from deleting files that they have write access to. It happens sometimes, but your people are just going to have to learn not to delete things that they need. If they were dealing with paper documents and files, they wouldn't shred documents that they might need later, would they? So why would they delete files on a computer that they might need. The answer is education (for yourself and your users), not trying to come up with a technological silver bullet that prevents people from doing something stupid.