FileZilla can easily be modified so that it doesn't create so many connections to the server, and hence you will not get blocked.
To modify FileZilla's max concurrent connections globally(no matter what site you connect to):
1. Go to the top drop down menu and select "Edit".
2. Go to "Preferences".
3. In the new window there is a side menu - from there you need to select "Transfers".
4. You will see on the right hand side of the window the text box so that you can change the maximum simultaneous connections.
5. In the text box, replace the current value with a value significantly lower(I recommend 1-5)
6. Hit OK and restart FileZilla.
7. Done
To modify FileZilla's max concurrent connections only for a particular site:
1. Go to the File menu and then "Site Manager"
2. Select your site on the left hand side menu.
3. Go to the "Transfer Settings' tab on the right hand side.
4. Tick the box which says "Limit number of simultaneous connections".
5. Change the value in the counter below the tick box to a value between 1 and 5.
6. Select OK to save.
7. Disconnect(if already connected) and then reconnect to the server, so that the settings can take effect.
If you are still having issues with too many connections to the server, you may need to have a look at any other applications you are using and make sure that they are not the cause of the issue.
