Mark Squillace, Eric Biber, Nicholas S. Bryner, & Sean B. Hecht have published “Presidents Lack the Authority to Abolish or Diminish National Monuments” in the Virginia Law Review Online. PDF

An excerpt:

The narrow authority granted to the President to reserve land[11] under the Antiquities Act stands in marked contrast to contemporaneous laws that delegated much broader executive authority to designate, repeal, or modify other types of federal reservations of public lands. For example, the Pickett Act of 1910 allowed the President to withdraw public lands from “settlement, location, sale, or entry” and reserve these lands for a wide range of specified purposes “until revoked by him or an Act of Congress.”[12] Likewise, the Forest Service Organic Act of 1897 authorized the President “to modify any Executive order that has been or may hereafter be made establishing any forest reserve, and by such modification may reduce the area or change the boundary lines of such reserve, or may vacate altogether any order creating such reserve.”[13]

Unlike the Pickett Act and the Forest Service Organic Administration Act, the Antiquities Act withholds authority from the President to change or revoke a national monument designation. That authority remains with Congress under the Property Clause.