When the patio guys took out our old deck, they found among other things a board directly beneath the sliding door that had started rotting away. We were fine contracting out the gas line but figured we could take care of this project ourselves.
After several calls to various family members more knowledgable than us, we decided all we needed to do was cut through the old board in the middle of the joists and put in a replacement. We got some pressure-treated 2-by material from the local Home Depot along with some 1-by material, weatherproofing clear coat, and fireblock.
We applied the weatherproofing the 1-by material and while that dried used a Dremel multi-tool to cut away the rotten wood. It probably would have been useful to have a little more power, but the Dremel was available and cheap so we got it and made it work.
Once everything was cut away, we used our circular saw to cut the 2-by material down to size and fit it in the new hole in our house. Three-inch roofing nails were used to nail it to the floor joists. We then sprayed some of the fireblock around the edges to keep everything sealed and hopefully prevent the issue from happening again. We put the 1×12 weatherproofed wood on top. With a little effort, we got everything in place.