Presumably NPCs can tell how much / how often you use beseech and if you've been to that well too many times, it starts to dry up.

My take on that second paragraph is that beseech is going to be more reliable when you're asking for a smaller favor (slight need) and/or your character is not known a person who milks it for everything its worth.

Just like in real life, a small handout is easier to find than a really big one.