I don't have access to Trail of Cthulhu, so I don't have the full Gumshoe system on my hand, so I can only refer to Lorefinder. If a character, according to LoreFinder
When spending from a Boosted, skill, your pool increases by 1 point after getting the information or benefit at hand.
How do you ever deplete that Investigate Skill? For now I just scatter 2-points spent now and then. Was this the intention?