Sony DVD Architect 2.
After adding subtitles, then saving the project, then reopening it, the subtitles show fine when the file is played back from the timeline and on Preview. I then inserted a disc(DVD -RW) and clicked "Make DVD." When I played back the burned DVD-RW disc on my set-top player(subtitles turned on --- and tested with a movie), the video shows but without the subtitles.
Have you tested the issue with a different hardware player / player software?
You can test also with 'Subedit 1.51' if your DVD programm stream contains correct subtitle streams. Please take a look on how the subtitles has been flagged: LB, WS or both? http://www.videohelp.com/tools/DVDSubEdit
DVD needs a correctly flagged subtitle stream for each of the used aspect ratios.
For 4x3 program you need just a letterbox stream.
For 16x9 you need an additional widescreen stream or just a standard stream flagged for both aspect ratios!
Additionally test your hardware player configuration!
If your player setup doesn't match your TV's aspect ratio your player maybe fail by playing the false subpicture stream!
Since I don't use DVD Architect I have no idea how it works inside.
But by adapting my suggestions there should be a way for success!