Generally speaking, no. The easement cannot be extinguished but by methods allowed by the state in which the land is situated. Generally, the easement will either run with the land (i.e. follow whoever subsequently owns the land), or it can be extinguished by sale of the land. The strictures of easement law turn on the granting language. But, the fact that there are other entries onto his pasture can only be considered, and are not dispositive.

Your best bet is to look to the granting language on the document conveying the property. The fact that you own the property does not control the issue. Your property is called the servient estate. If the language indicates that the easement was intended to benefit the other parcel (the dominant estate), then the easement is likely to run with the land. Also, look for language such as "in perpetuity," or "binds the owners and their heirs, agents, successors, and assigns." If such language is present, the easement likely runs with the land, and the holder of the dominant estate is the only one that may terminate the easement. If the above language is not present in the document, the easement could have been extinguished when the land was sold to you. But, given the circumstances you provided, it seems that the easement benefits the land and cannot be unilaterally terminated by you.