This was originally a longer message but I edited it because I found the problem. I moved the files from the torrents and resume directories to another folder and Transmission ran correctly. I will move only a few tracker files this time and see what happens.

Next time please do not edit the original post. Instead reply with your solution.
It's simply how forums work and any posted explanation and diagnostics may help others encountering the same problem,
TIA.

Sorry about that. What I found out is that Transmission in a Buffalo NAS can only take a certain number of tracker files loaded before it no longer runs. In this case, there were more than 500, with 20 downloading and around 20 queued. Transmission-daemon would run momentarily before shutting down. I verified this when I ran it followed by ps -A: it would appear in the list of running tasks but after a few seconds would disappear when I ran ps -A again.

To solve the problem, I did the ff.

1. uninstalled Transmission

2. went to the transmission-daemon folder in .config to move the contents of the resume and torrent folders to another place

3. moved the folders containing the seeded and incomplete files

4. deleted the transmission-daemon config folder

5. re-installed Transmission

6. put back the folders containing seeded and incomplete files

7. reloaded only the tracker files in the torrent folder for which files existed in the incomplete folder (because if I loaded all of the tracker files I'd end up with the same problem)

8. did a force re-check of each file in the seeded and incomplete folders so that I didn't have to download each one from scratch

The problem had nothing to do with a defect in the Transmission settings file or the client in my PC, which is why I decided to delete my original post. From what I gathered, Transmission can only have a certain number of tracker files loaded, whether paused, queued, seeded, or downloaded, and this is probably affected by the CPU and memory constraints of the NAS. Given that, I will very likely keep the number of tracker files loaded small and put the rest of the tracker files in another folder for loading in the future.

Thanks for posting your account of things. I would think that maintaining 500+ torrents would put a strain on any machine. For next time, with Linux there's rarely any use for removing and re-installing software. Before you do remind yourself an application may log warnings that may contain clues. For Deluge they should be in the users home directory: /home/username/.config/deluge/logs/.