The only thing that I could find to lower loyalty is month end changes. So, if you hired someone from the cafe and their loyalty drops it is only because you didn't treat them at least 15 times before hiring them.
If you hired someone from the inn/lodge, their loyalty is going to be 10 because everyone starts at zero and everyone increases by 10 when you hire them. I haven't tested the amount of raises that would be needed to raise their loyalty by much. What I have tested is that agreeing to the increase when they ask only gains 1 loyalty, but I haven't checked every mate and every level from 10 - 100 in loyalty.
I did enough testing using the mates from the cafe to know that they will only ask for a raise once their loyalty falls to or below 30. What I didn't get around to testing was if there was a level that would always cause the to leave you when a battle started.
Nothing that I have checked except the end of the month event seems to lower loyalty. Not having the funds to pay their wages didn't seem to have any additional effect. Sailing without food and water didn't seem to have any effect on their loyalty.
If you by chance miscounted the number of treats and hired someone after 14 treats when they needed 15, their loyalty will fall from 94 (6x14 plus 10 for hiring) at about 6 or 8 points per month. You probably won't even know it until they reach 30 loyalty (about 8-10 months). At that point, if they ask for a raise, you are probably better off to refuse and then run to the cafe and treat them 15 times to make sure you have 100 loyalty. Remember there are some mates that only need to be treated 3 times total to be hired at 100 loyalty.
Sorry, I didn't mean to run on and on, and the short of it is that there really isn't anything you can do to make loyalty fall faster (that I have checked yet). You could give them a cheap ship and enter battle and hope they leave you. If you want them back it is just a matter of finding them again.
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