As far as I remember, WordPress does not impose a limit on the level of depth of the sub(sub…)menus.
Depending on the amount of menus items you have and still want to create, you may be reaching the limit of how many POST variables the browser can submit to a server at a time (limiting the number of menu items, either sub or non-sub, you can create/save) – WordPress menu item limit forum topic.
And Parabola supports at least 4th level submenus without problems (that’s how far we’ve tested it). You can see this in the theme demo (the “Dropdown” menu).