The problem was (supposedly) fixed in February in a 1.18.7.x release.
Make sure you are running a current version of Plex Media Server. Check Authorized Devices to verify installed version.
Version 1.19.1.2645 is available via plex.tv/download. You want the Intel 64-bit package.
The Synology FAQ has information on manually installing packages (versus using the version available in the Package Manager). See FAQ 3a.
The Plex Media Server Announcement thread has information on the latest releases. To be notified of a new release, subscribe to thread. Scroll to the bottom of the thread and change “Normal” to “Following.”
Note the portions regarding media location. Do not put your files in /Plex or in Synology’s pre-defined media folders (used by their own applications). Doing so will cause problems down the road.
I also have the Synology DS1019+ and am running Plex 1.19.2.2737 currently. It seems to transcode h264 just fine, but when trying to transcode a h265 file, Plex says
This server is not powerful enough to convert video.
despite the DS1019+ having a hardware decoder for both h264 and h265:
H.264 (AVC), H.265 (HEVC), MPEG-2 and VC-1; maximum resolution: 4K (4096 x 2160); maximum frame rate per second (FPS): 30
The test file:
Codec HEVC
Bitrate 2782 kbps
Bit Depth 8
Chroma Subsampling 4:2:0
Coded Height 1088
Coded Width 1920
Color Primaries bt709
Color Range tv
Color Space bt709
Color Trc bt709
Frame Rate 23.976 fps
Height 1080
Level 4.0
Profile main
Ref Frames 1
Width 1920
Display Title 1080p (HEVC Main)