Your parents will not lose the right of way. It doesn’t matter if they don’t use it for the next 50 years, a right-of-way noted in the deeds is only extinguished if both properties come into common ownership or if the two parties mutually agree. The latter seems unlikely. It doesn’t matter that the neighbour fences part of it off, they still have the right over it because offence can easily be removed if the court orders it.
There is no easy way of resolving the issue of where the boundary should be and if neither party can agree, then it is a case of the matter going before a judge and the court determining the boundary. Each party could have their own surveyor who would make representations to the court and the court would decide the issue based upon the information in front of it.
Alternatively, try to avoid court and get perhaps a different surveyor to decide the issue and both parties agree on being bound by the surveyor’s decision.
Please note that if there is a right-of-way over this pathway, then the right-of-way cannot be divided whereby part of the pathway belongs to the neighbour and part pathway belongs to your parents. The issue here seems to be the extent of the pathway which the neighbour seems to be saying is narrower than it is.
Ultimately, as is always the case, if there is no meeting of minds, whether that is with the help of a boundary surveyor or not, the only option open is to take the matter to court.
Your parents might want to check all the house insurances to see if they have legal expenses cover that would pay for the legal costs of dealing with this. If they have, then pass this over to the insurance company to deal with.
Can I clarify anything for you?
Please don’t forget to rate the service positive. It doesn’t cost you anything but helps me greatly, I get paid!