I'm not a solicitor but if the fence in question is the march fence between two holdings then maintenance is usually a shared responsibility on a 50/50 basis unless specified otherwise in the deeds.
So the farmer may be happy to arrange the work if you are prepared to pay your half but not to take it on as once he does then he is effectively accepting full replacement and repair costs.
Damage done by escaped livestock may be sued for but will cost you money to do so and you'd honestly be better to stay on good terms with a farming neighbour and use the money to contribute or offer to arrange if he pays you his half.
That's my understanding anyway. As I say I'm not a solicitor let alone a specialist in agri-law but a march is usually dual cost unless one takes it on voluntarily. I'm pretty much maintaining/replacing all 3 of my march fences aswell as my own roadside and internal ones, because the farmers aren't interested and the ponyowning neighbour is unduly optimistic to the point of stupid about how he manages grazing beside a longstanding stud