Your landlord is required to provide a fit premise that is safe and liveable.  Water damage may not be considered a safety concern, but is certainly a big problem for the property.   Untreated water problems can lead to serious problems that can lead to mold growth, cracked foundations, dry rotted wood etc.
If you feel your landlord isn’t being fair, you can always file a landlord complaint with the RPA.  That or beg him to be responsible.  He’s probably avoiding the repair due to the possible high cost associated with it.  Although, he’s rolling the dice– if he lets it go, it will be VERY expensive.