You need to request a "full" copy of your insurance policy. Look at the "Exclusions" section to see what exclusions there are related to plumbing leaks. Also, in the "Perils Insured Against" section, look at what is not covered related to plumbing leaks. Make sure you read through the entire policy including any endorsements because there could be exceptions and changes in coverage. I've been in the insurance industry for over 20 years and based on the facts you describe above, this sounds like it would be a covered loss. That said, there are typically exclusions for water losses that are long term in nature. Most states require an insurance company to quote the policy language they are relying on when denying your claim. If the adjuster is telling you the claim will be denied, make sure you ask the adjuster what policy provision they are relying on specifically. What page is it on, what section and subsection? And ask the insurance company for a letter in writing explaining the coverage determination.
Also, insurance companies will sometimes hire independent adjusters to do their field inspections and they may not be employees of the company, and have no authority to make coverage decisions. If that is the case, speak with the desk adjuster who normally is an employee of the company. This is the person who will typically make the final coverage determination.
Finally, document EVERYTHING. Take pictures of everything, get receipts, etc. The more documentation you have the better. And make sure you do everything you can to mitigate your loss. Most policies require this. Good luck.
