Each minion has specific zones in which they should drop. https://imgur.com/OgXrU0Z is a handy little picture that will show you the zones you need to be in. You can also find this information by opening up the Minion Guide from the main menu, and it will have a little button under the minions that says "Open the Yo-Kai Medallium".
A friend of mine said that they did about 40 FATEs on their first minion in the wrong zone completely, and they did manage at least one drop - so it sounds like you can at least get them, but it's INCREDIBLY slow and painful if you're not in the right area.
If you're in the correct zone, it really shouldn't be that bad. My worst streak took me 27 FATEs to complete one weapon. Others were as quick as 16 FATEs. Obviously results may vary, but this does seem to be around the norm from speaking with others.
