http://www.heathrowexpress.com/content.asp?SID={BE4AD200-6D47-49E6-98A8-E587F42A6194}&pageid=69

Under Section 3.5 of the Conditions of Carriage states:

"Single tickets are valid for three days. Unless dated for a specific day of travel, they are valid on the day of issue only."

If you book online, you state the date of travel. In that case, it seems to be only valid for that date and all you could do is to get a refund under their policy.