Posted: 03/09/2014 at 21:22
Sadly we live in a world now were some neighbours don't seem to see or care what problems their actions cause to others.
I had a similar problem only I was the one who wanted to level out my lawn. The dividing fence is wooden panels with concrete posts, I replaced the bottom of the fence with a 1ft high concrete fence as fidgetbones suggests, after explaining to the neighbours, why, and then put the wooden fence on top of the concrete. We agreed when the wooden part needed replacing we'd use panelling 1ft shorter, which is what happened. Problem solved.
Your fence may need the wooden posts replacing with concrete as these will last for all eternity.
I paid for the concrete part though, which was only fair. When the wooden panels needed replacing, although I offered to pay half, they insisted on paying for it reasoning their children had hastened it's demise by kicking footballs against it...two happy nieghbours.
I'm happy to be wrong but some dividing fences are jointly owned, the deeds to youir house should hold this information, however, if one neighbour decides to pay for the replacemet of the whole fence it becomes their property and their responsibilty to replace it. Your neighbour may not know this so I'd let them work this part out for themselves.
The issue in your situation is the neighbour damaging your property. Talk to your neighour first and see if you can reach an agreement to replace the fence with concrete fencing at the bottom to keep the neighbouring garden, in the neighbours garden.
This doesn't answer your Q but if the cost is shared, it will then be jointly owned placing part responsibility on your neighbour to keep it maintained.