That seems to be a problematic situation indeed. Could you please send your logs.db and out.txt files to support@insynchq.com? These should be in ~/.config/Insync.
To follow up:
Is this problematic Sharepoint folder being constantly modified (whether Insync is running or not)?
Is there a noticeable pattern when it ends up in your local trash?
Could you clarify what you mean by “… while the others do not synchronize” – by “others” did you mean the other folders, as in it stops syncing altogether after the deletion?