Unless you check the box "always open in multi-user mode" then Quickbooks opens a file in single-user mode every time.
This is by design and does not require troubleshooting.
Update: mhache's instructions were right on the money in this case. We found that 2 of the systems were hosting the file in multi-user mode. Once we had only one workstation hosting the file the single user mode became almost non-existent. Thanks everyone for your input!
Thank you.