The best way to fix a deteriorating foundation?
That corner looks like it was screwed up from the start with the way that bottom corner brick was laid. I would be drilling a number of holes in that bottom brick's mortar and removing it. Scrape away all that patch stuff from the slab.Then hammer away at that corner to break away any weak concrete. Then I'd get some 2x4's or 2x6's and re-frame that corner level with the existing slab and support the framing with a a few stakes/rebar. Drill and screw in a few Tapcons to act as mesh/rebar. Mix up some real concrete and re pour that corner. After it hardens, get some mortar and install that last brick correctly. Fill in any other voids in the brick mortar. This is a bit more work that you were probably hoping for but this is what I've done up North where they have harsh winters and it holds up real good.