TNG has worked with the same folder permissions for over a year and a half but suddenly stopped. After some searching I found Synology's DSM update has security changes that may affect TNG's ability to write to certain folders. This is dependent on how permissions were set up originally on the parent folder, i.e. are child folders permissions inherited. (My permissions were not inherited)
TNG allows admin users to create custom media collections. These collections were affected by the Synology update on my system. The custom media folders on my site are, births, deaths, marriages and wills. After numerous failed attempts to add media, I changed permissions on the folders to 767 and everything started working again. Instructions for changing permissions are in the Install TNG on a Synology DSM post.
Check that http permissions are read/write on the TNG folder. If not, new media folders you create, in the future, may have the same problem depending on how they are created.