There seems to be confusion in Ohio on this matter:

CLEVELAND, Ohio -- The growing popularity of early voting raises the question of what happens when someone who casts an absentee ballot dies before Election Day.

Does the vote still count?

The answer, it seems, is yes, though Ohio election law does not specifically address the question and the Ohio Secretary of State's office issued a ruling only after receiving inquiries last week from The Plain Dealer. A survey by the newspaper found differing opinions among elections officials in some Northeast Ohio counties. The elections director in Medina County believed the ballot should be invalidated, while the Lorain elections chief said the vote should count.

Cuyahoga County Elections Director Jane Platten sought advice from the Ohio Secretary of State's office, and said she received conflicting opinions. At first, an attorney for the state office advised her that a ballot must not be counted if cast by someone who is not a qualified voter on Election Day.

But later another state election official overruled that and told her the ballot counts.

Matt McClellan, a spokesman for Secretary of State Jon Husted, told the newspaper Thursday that the fact Ohio law is silent on the matter means election officials should count a ballot even if cast by a voter who subsequently dies.

"Absentee ballot still counts if voter dies before election", Harlan Spector, The Plain Dealer, October 22 (original and updated)

http://www.cleveland.com/metro/index.ssf/2012/10/absentee_ballot_still_counts_i.html

That there is confusion on the matter in Ohio does not imply that either side's argument is equally legitimate, or that there is no correct vs. incorrect answer on this question.  I am not an election lawyer and defer to anyone who is. 

But I find it unfathomable, from a strictly logical standpoint, to think that a validly cast absentee ballot cast during the period in which absentee voting is permitted could somehow not be counted, simply because the person who cast the valid vote died prior to Election Day.  

The legal implications of the concept of "Election Day" may need some tweaking in a day when so many votes are cast prior to it.