Hello,
I had the same problem. http://SyncTables.com was the solution. This SW can copy and sync tables in databases. It supports MySQL, Access and MSSQL. To connect to databases at a webhoster an http-tunnel can be used.
I also use it to download new orders to my local database as it can synchronise tables. In this case it only downloads changed records determined by a last-modified-column.
I hope this helps!
The cyberdwarf š