Roof help

We just bought a 4 floor limestone and have a leak into the 3rd floor front room. The 4th floor is on the back of the house so the water seems to collect outside of the little roof right on top of the 3rd floor room. We had the whole roof reflashed and had a patch done to that part of the roof, but the roof still wavy and collects a bit of water. Is there anything else that can be done to solve this problem?

We know we need a roof sooner than later, but cannot afford to do the whole roof now. The Inspector and our GC thinks we can survive with it at least 2 more years. Also, can someone recommend a good roofer.

Thanks