I'm not sure if anyone else is getting this problem but it seems that the threads on MyBB 1.6.14 seem to be self closing for some weird reason.
At first I thought a Moderator of mine did it, but it happens randomly.
Are you able to list the steps to reproduce the error?
This forum is running 1.6.14 and I haven't noticed any 'autoclosed' thread yet. So probably your moderator did it and someone deleted logs. Or you have a faulty plugin.
But as dragonexpert said, if you're sure that the issue exists in MyBB itself, provide steps to reproduce it.
You may also want to look at Admin Permissions and make sure no one except for you can Manage Admin or Moderator Logs as this is how they can get pruned.
I figured what it happened. Was because the Custom Moderator tools were affecting the thread Open/Close status. I had a Custom Junking Mod tool. I made some changes and fixed it.