The posts are saved in a XML file inside the "db" folder. You must be sure that the "db" folder have permissions for writing.
To set the permissions for writing you need:
FTP programs ("clients") allow you to set permissions for files and directories on your remote host. This function is often called chmod or set permissions in the program menu.
In the first image, look at the last column - that shows the permissions. It looks a bit confusing, but for now just note the sequence of letters: