Normally, easements do Not include an obligation to maintain, by either party.
No one mentioned this, and it's a crap shoot, but have you looked at your counties public works GIS system? Being that it is a multiple party easement, the County could have taken the easement to ensure access. Many counties don't have this kinda info easy to find, but some do. There are cases where a multi party easement is transferred (or taken) by the county.
Although I do believe Pinion, it's easy to have record of an easement drop away over the coarse of multiple sales, regulation on how far back a title search goes, property splits/combining, ect.
If you do successfully block his access, and he Does have legal access, he May be able to come after you for damages, inadditon to you allowing it.