Nick
I believe that the reason you are having issues, is due to permissions on non-admin users, and you might need to install the sync engine to each individual profile.
Furthermore, I have confirmed that we do not provide any level of support for Terminal Server setup. If the install works fine on an administrator profile, with Full permission, then here is where our support will stop. Unfortunately you will need to determine to root cause of the problem with your other users.
These types of issues require that you need to be able to debug which specific directories and folders needs to have permissions set properly and also ensure that the click-once install does not fail.
You can can find more information on similar cases HERE