There are a few things to consider when it comes to whether or not a slow leak is covered by insurance. The first is the type of insurance you have. Homeowners insurance typically covers water damage, so if the leak is coming from within your home, it should be covered. However, if you have renter's insurance, it may not cover water damage unless it's specifically listed in your policy.
The second thing to consider is the source of the leak. If the leak is coming from a pipe within your home, it will likely be covered by insurance. However, if the leak is coming from an outside source, such as a broken sprinkler head, it may not be covered.
Lastly, you'll need to consider the amount of damage that has been done. A small leak that has caused minimal damage may be covered by insurance, but a large leak that has caused extensive damage is less likely to be covered. If you're unsure whether or not your particular situation would be covered by insurance, it's best to contact your insurer directly and ask.