I don't believe this is possible in version 6.x. It is possible in version 7, which will be released soon (sometime this month most likely). Simply don't check Can remove files in version 7 and affected users will be able to upload a new version, but will not have the ability to delete a file.
Version 7 is not a long term support version like 6.3, so it may be slightly less stable depending on the features your site is using. Would recommend thoroughly testing if you go this route.