The rules do not specifically say, but all indications are that they "always contain what you need" in them.

Here's what we know...

A Component Pouch costs 25gp and...

is a small, watertight leather belt pouch that has compartments to hold all the material components and other special items you need to cast your spells, except for those components that have a specific cost (as indicated in a spell's description).

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The rules talking about Spell Components treat a Component Pouch and a Spellcasting Focus the same way...

A character can use a component pouch or a spellcasting focus in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.

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This indicates that you only need to worry about possessing zero-cost components if you do not possess a component pouch or spellcasting focus. This may become relevant if, for example, you are kidnapped by the Drow, stripped of all of your possessions, and escape with nothing but the shirt on your back.

Next, while this is not part of the Sage Advice compendium and Crawford-Tweets are no longer considered "Official Rulings" until they make the compendium...he is still useful for clarification...he made the following Tweet.

Q: How do you handle components that don't have a cost but can't be stored? E.g. the flame for Heat Metal.

A: If you're using a spellcasting focus or a component pouch, free components are abstracted away.

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While that was not a directly related Question and Answer...the idea that "free components are abstracted away" is pretty clear. You have a component pouch, therefore it is assumed that you have the zero-cost components that you need even when it doesn't make sense for that thing to go in a pouch.

Finally, a touch of logic: a Component Pouch is more expensive than any spellcasting focus (though it does leave your hands free when not actively casting a spell). If, after buying it, you had to run around every single time you leveled on mini-quests to stock up your component pouch--then the pouch is patently inferior to a spellcasting focus. It doesn't really make sense that the rules would treat a Component Pouch as equivalent to a Spellcasting Focus if it, ultimately, is not.