The burden is theirs, not yours
Most service agreements exclude conditions that were known or reasonably discoverable before coverage began. That wording matters: the company generally needs to show you knew, or obviously should have known.
What actually beats this denial
A home inspection report from before the contract started. A technician statement describing a sudden failure. Maintenance records showing the system worked. Any of these undercuts the claim that the condition was pre-existing.
Check the waiting period math
Companies sometimes blur the waiting period with pre-existing conditions. If your waiting period ended before the failure, ask them — in writing — which specific contract section they are relying on.