There are certain ways you can attempt to fix a chunk error:
For server use:
It could be that your TPS is set low. TPS is much like FPS but for the server. It cannot go above 20, and it should stay at 20. TPS stands for Ticks Per Second. This applies to singleplayer, as it runs a sort of local server when you load one, this is to allow opening to LAN.
Common symptoms of low TPS include the sky jumping back a little bit every second making it look laggy and extending length of day/night cycle, mobs/entities (not including players) moving unusually slowly, all entities that can take damage take it much more slowly with delay, all entities effected by gravity falling slowly in choppy little bits, players seemingly teleporting around in multiplayer (purely visual), blocks difficult to place/destroy (multiplayer and in extreme cases in singleplayer), etc.
Check your game's Ticks Per Second by typing
If the speed is set to larger then 3 then we may have found your problem. Set it back to 3 if it is set higher.
With a little research I think WorldBoarder may solve your problem it allows you to fully generate (fill) your world all the way to the border, filling in any missing chunks, including a configurable buffer zone just outside your border.
With a little help you can also make another possibility possible. If you were to create another account and keep that account in the needed chunks then it is possible that the chunks won't unload keeping them fully functional. I Found a great video that could go hand in hand with this idea: Super Chunk loader
If this is the most important part in your world that isn't loaded, you
could place it in your spawn chunks. Spawn chunks stay loaded in
your world because they are stored in your memory.
You could also use the commonly talked about hopper chunk loader which may keep the chunk loaded all the time. Hopper Chunk loader As an edit to your comment on how loadding your whole map would be an inconvenience, I found another Chunk loader that can be set to load only one chunk: Here is the link: Minecraft 1.8.8 Remote Chunk Loader Explained
It is possible and could be likely that you have a corrupted chunk even if it says you don't. There are different types of corrupted chunks, but there are ways to patch, fix, and delete depending on the problem. This would require MCedit to fix. I would suggest copying this part of your world with commands or Woldedit before you try this, if you still can. If you close your server for a bit and load it up in single player, you can attempt to patch it using this method: Corrupted chunk fix for single player You may need a similar fix like this, but not this one, so this will only get you to the starting line and help in your search.
As a final thing I found a mod that may do what you want. It is called CodeChickenCore. In this mod it has something called ChickenChunks, This is what it should include: This introduces a new block called the “Chunk Loader”, which allows chunks to be loaded in memory at all times. It is very convenient to use as it comes with a special GUI for configuring chunk loading. Chunks are also free to load.
I found this download here.