Thanks for your reply BH. There is usually more than a half hour between when I enter the notes on my laptop while at church. Then once home, I post the notes to the church website from my desktop. I am not accessing the shared folder at the same time.
My point is not about access a shared folder at the same time, though that can be an issue if a file is open on one computer and then you try to access it on the other. What I was pointing out is that when you start a another computer up, it has to sync all the files first before you try to access them in order to see all the changes. Again, that may not be your problem. I'll say the sync issue another way: you edit a file, this being e-Sword, a topic file, you save it into your cloud drive and close e-Sword. Hours later you start another computer, and immediately start e-Sword and try to access a changed file. If the cloud service has not yet synced the files, you will not see that proper changes. Things that can affect syncing time are the speed of your internet connection, the number of files in the folder that needs to be indexed and checked, and the size and number of files that need to be synced. Dropbox syncs the smallest files to the largest. I don't know what OneDrive does. If there are a lot of large files such as pictures which are shared, this may interfere with sync speed.
I have used shared files with e-Sword for quite a while without an issue using Dropbox. I make sure that Dropbox has finish syncing files before using any program which depends one a shared folder.