It's usually a bad idea to have a bored protagonist (or viewpoint character). Often a bored protagonist means a bored reader, and perhaps even more often than that, it means that the writer didn't take the time to think about what the character should be doing. It's lazy writing.
It's also just problematic because it means there is no active, present goal. And/or there is no active, present antagonist. Which usually leads to scenes "flatlining" (no rising action). This will slow the pacing down (and not in the good way), and if it takes up a lot of word count, will bring the story to a grinding halt. A lack of goals and antagonists creates a domino effect that usually results in a lack of everything else related to a strong plot--a lack of conflict, a lack of progress, a lack of crises, a lack of tension.
Perhaps just as bad, is often the character's boredom segues into terrible play-by-plays, where nothing meaningful happens.
Boredom in a protagonist is typically a lost opportunity. Even if nothing "important" is happening in the plotlines (which is something that should give you pause in and of itself), the protagonist could still be doing something minor that is important to him or someone he cares about. This reveals character, and is therefore more interesting than him wasting time doing mundane things or doing nothing. Something as simple as giving him a hobby he loves, is better than boredom.
9/10 you do not want a bored protagonist.
But . . . as always, there are exceptions. These are the 1/10 situations.
So let's go over those.
