How can I fix this leaky roof over a covered open air porch?
That little shingled roof under the deck would be a really bad idea, because replacing the shingles will be next to impossible. So it smacks of an after-though project and I'd venture to say that they didn't properly flash that roof to the siding, meaning the flashing needed to go UNDER the siding. Fixing it properly now could be really expensive because it may require removing the deck to get at the upper corners. What they likely did was just run a bead of caulking along the roof-to-siding seam, and that didn't last long. What you can probably do now if you don't want to tear anything out is to preemptively remove and replace that caulking every once in a while, maybe based on how long it had been working for you until now. Use a butyl caulk, they last longer in applications like this.