Make No Concession
If the probable occurs, and we have another contested vote, there are two modern precedents which bear considering. In 2000, Al Gore took Nixon's prompt and conceded relatively quickly for fear of disrupting the fabric of the national life any further. Nixon was fond of saying that Eisenhower urged him to demand a recount but that he would not cause a constitutional crisis by contesting his loss in 1960. Turns out Eisenhower never urged the recount, but the logic behind the Nixon/Gore concessions remain the same: the country cannot withstand a contested presidential election.
In Gore's concession speech, he cited Douglas' remark to Lincoln, who had just beaten him in a presidential election, "Partisan feeling must yield to patriotism." Indeed it should, but which benefited more from the 1960/2000 concessions: partisanship or patriotism?
Hindsight clearly indicates the former was the beneficiary and that the latter suffered greatly. In three short years, Kennedy would be assassinated, a crisis which catalyzed the civil unrest of the 1960's. Moreover, Nixon would ascend to the Presidency only to cause an arguably greater crisis of leadership. It's awfully specious to suggest that Nixon's victory in 1960 would have prevented Watergate, but we can be certain that Jack Kennedy would not have died as he did.
More reasonably, if Al Gore had held on to his legal fight and won the election, there is no doubt that he would have not polarized the nation even further by pushing a conservative social agenda and a liberal economic one, and clearly, he would not have lead us into war in Iraq.
In the wakes of these two modern concessions, events would unfold that would test the limits of American patriotism. Clearly, the country will stand to gain much more in the long term with a prolonged contest of the election results than it will with another short-sighted concession, which is made more with an eye to fighting another day than with an ear to the public's needs, no matter how much lip service is paid to that notion.