The Sindarin dual was almost certainly derived from the same primitive form ✶ata as the Quenya dual ending -t, indicating this ending was ancient in form. The other Quenya dual, -u, would not have been active in Sindarin since final vowels were lost.
Tolkien stated (Let/427) that this ending was archaic and lost, but did not state when it disappeared. Most likely, though, the ending was still active in the First Age. The ending appears in the day-name Orgaladhad “Day of the Two Trees”. Since the Sindar had no direct experience with the trees, this word was likely adopted from its Quenya cognate Aldúya when the Noldor and Sindar were reunited.