Storage/Parking away from the house???

X12AEsq wrote:
Consult a local attorney. Possibilities: non-conforming use (parking the RV) may have begun prior to that zoning limitation, hence grandfathered; parking RV on neighbor's land with concurrence for 20 years may have created a permissive easement in your favor; depending on adverse possession statutes in your jurisdiction, it may actually have given you a colorable claim to ownership of that 1 foot strip.

No, you will not win a claim for prescriptive easement. Among the elements necessary to win such a claim would be the fact that rectifying any encroachment would create undo hardship on the party encroaching and that the encroachment has been ongoing for a long period of time. Obviously, since it is an RV it can easily be removed (unlike if you accidentally built a barn one foot onto their property) and the encroachment has not been ongoing, since the encroachment ends every time you take the RV on a trip.
Most people would not like losing part of their land. If it was the neighbor coming after you for a running foot of your land, most of us would fight it tooth and nail. The reason the neighbor doesn't want people encroaching on their property is immaterial. It's their property.