Most likely this is occuring because the database file is being locked by the web server when it is accessed via the web site. This issue is a known problem and is inherent to Access.
What usually occurs is an FTP request gets refused because webserver has an open connection to the database and is in the process of updating the file. Also, if an FTP transfer is in progress and the web server opens the file, the FTP transfer is aborted because the file has changed before the transfer was completed.
To get around this, the web server needs to be either stopped, or the site needs to be prevented from opening the database while the transfer is occuring. Stopping the web server is generally not done, as it stops all sites on the server. Stopping the web application is the preferred method, as it allows the other sites on the machine to continue to run uninterrupted.
To stop the web application from using the database, usually you would need to code in a "maintenance mode" into the application. This mode would close any current connections and/or refuse to open new ones while maintenance is taking place. Some web applications have this built in, but most do not. Since we are not familier with the details of your application we cannot make a determination whether you can immediately do this or if modifications must be made first.
Other options include writing a transfer program to query the database while it is online and transfer the data without using FTP. This can be done in ASP and other tools.
If there is an emergency and you require a download of the database file while it is locked, we can stop and start the server to free any locks, but as mentioned above, this is not something we can do on a regular basis.