Recently, Shopify introduced a fundamental change to how complex navigation menus are constructed for your store.
Previously, you would have had multiple menus for each dropdown on your store, like this:
Now, Shopify allows you to build your entire Main navigation structure in one physical list, using a nested arrangement of links to build your dropdowns:
Updates were rolled out to all of our themes at the appropriate time, so that there was no service interuption for our users - people with older theme versions continued with the old method of arranging menus and new store owners got both the new theme version and the new method of building menus.
However for a small number of stores running older theme versions, it is possible you might encounter a problem when updating your menu structure.
You have recently updated your theme and are no longer seeing drop down menus on your store, it's because you need to build the Main menu in the new style, by conjoining your previously separate parts into a single menu.
Your menu has suddenly stopped working (ie drop down menus have disappeared) and you haven't recently updated your theme, you have two options:
You're making changes to your navigation structure which don't seem to be reflected on your live store, it may be because the new menu structure has been triggered on your store. Check you're making changes to your one Main menu, not the old constituent parts of your menus
Check out Shopify's guide to updating your theme: https://help.shopify.com/manual/using-themes/organizing-themes/updating-themes
Full instructions on creating dropdown (or similarly structured) menus: https://help.shopify.com/manual/sell-online/online-store/menus-and-links#create-a-drop-down-menu