Just a suggestion.. Possibly make a small area with something else but grass. Small stones, or bark to do their duty. If you put their duty on the new small area they will continue to go there. Go out with them a few times when it is redone to re-train them, it's not that difficult. Eliminates always repairing lawn each winter. Look for landscape ideas on HOUZZ, or pinterest. They do not need an extreme large area.
You could avoid this problem by walking them and picking up after when it happens.
Hi Adrienne! A good question and here are some links for helpful information.