The initial question – just on case it is this simple – is do your users have the permission set to ‘Can download other file type attachments‘ which you can find in the ‘Viewing; section of the permission ste records?

If it is not that simple a few questions to start off with…

Are you saying that they used to be able to see attachments but no longer can or are these all new?

What versions of the core SP and the File Uploader (plupload) plugin do you have active now and what version of SP core did you upgrade from?

What SP theme are you using…?