Thought I'd report back.

I tried @Sherwood's suggestion and it worked. I scrubbed down the public path outside my house and did the same to my fence. I scrubbed thoroughly with a broom and hot water with a mild amount of bleach.

However, this might not be the reason it worked...

While I was cleaning, a couple of local dog walkers saw what I was doing and no doubt saw the look of anger on my face. One regular dog walker even crossed the road to avoid me while I was cleaning (and cursing). My guess is that one of those dog owners could have been the culprit and is now thinking twice before letting their dog mess in front of my house.

Either way, it seems to have stopped for now.