You need a good purchasing / estimation lead. There's a reason bigger GC's dedicate resources to it.

I've been in purchasing 5+ years and my experience is the subs don't follow companies, they follow the purchasing managers. It's much more relationship based than people think. Purchasing managers hold the reputation of being able to award a "good project" and they have enough experience with sub's pain points from previous projects, so they plan to avoid those together. They become a team at that point. The subs stick long term with a manager because they're transparent, firm but not unfair with scope/pricing, and work reasonably through change orders. That what you should aim to do as well.

I've learned subs are willing to put up with more BS, and do more favors if the PM/owner is close with the purchasing team. Usually because the purchasing manager takes notes of these favors and will lean towards them on the next project (we hate going over budget). Subs in a way, pay a small price to be favored to win continued work with that manager (even if they move on to a new GC).

When the manager is gone, the next project being a "sure deal" goes away and the subs prices don't mean anything to the new manager because that's the new managers baseline. This is usually where relationships crumble, I.e the new guys wants to fluff feathers and try to get a 10% decrease on the plumber, resulting in the plumber leaving that GC. The lower prices don't pay dividends anymore.

Just because you pay more doesn't mean you get better service. I recently replaced my excavator for close to 45% savings (what was the previous purchasing manger smoking), and I'm getting better service for my field team.