I'm guessing that Koei simply applied a limit.
The one thing I didn't test when I was checking how the loyalty works was the effect of giving a large raise. If you give a raise when they ask for one it is always 10 more per month, but you can raise the wages at most any time and it doesn't just have to be when they ask.
If fact giving them a raise when they ask did very little for their loyalty. First, for them to ask for a raise their loyalty has to drop to 30 or below. Saying yes only added 1 point of loyalty in every case that I checked. Like I said in the paragraph above, I didn't check to see what giving them a raise at other times would do for their loyalty.
To summarize my findings, you can always hire a mate in the cafe at 100 loyalty if you treat them 15 times OR if you pay attention to how many times it takes for them to say "I hate to brag...". If you have to treat them 6 times before they say that, you will need to treat them 9 more times to hire them at 100 loyalty. If you have to treat them 3 times before they say that, you will need to treat them 5 more times to hire them at 100 loyalty. If you only treat them twice before they say that, you will need to treat them 3 more times to hire them at 100 loyalty. If they say that when you first treat them, you only need to treat them 2 more times to hire them at 100 loyalty. This applies to any mate that you hire in the cafe/pub.
Any mate that you hire in the lodge will start with a loyalty of 10 and may ask for a raise before you leave the port. Remember they only ask if their loyalty is 30 or below. The secret to getting a mate that you hire at the lodge to 100 loyalty is to "trick" the AI by sailing until the month changes twice.
What happens with a mate that is not at 100 is that their loyalty drops every time the month changes. Since the mates you hire at the lodge/inn start at 10 loyalty it should only take a couple of month changes for their loyalty to fall below zero. When that happens the game changes it from a negative to 100 loyalty.
I still haven't found a way to lower the loyalty of a mate that is at 100 loyalty. I've tried sailing without food and water, and sailing for months without any gold to pay them and still their loyalty stays at 100.
You may be better off to say no when they ask for a raise and then hire them again. If you hire them a second time their loyalty will start at 20. Hiring a mate adds 10 loyalty regardless of where you hire them.
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