I tend to not "select/activate" a sheet if I don't have to to optimze
the codes. In this case, the code works  fine during the search
operation, but fails because the sheet that it needs to plop the rec'd
date on is not the activesheet, therefore it's dropped on the wrong
sheet (activesheet).

Like AJ said you have to specify which sheet to fill the date  on...
as "Sheets(k).Cells(rngA.Row, [e:e].Column).Value = recdate.text"

Here's the new code with the correct sheet explicitly defined:

Sub testRangeName()
Dim rngA As Range
Dim k As Integer
Dim aSheet() As Variant
Dim strTest As String

aSheet = Array("Telxon Repair History", "3870 Repair History", _
"SF51 Repair History")

For k = 0 To UBound(aSheet())
Set rngA = Sheets(aSheet(k)).Cells.Find(What:=recpo.text, _
SearchDirection:=xlPrevious, SearchOrder:=xlByRows)
If Not rngA Is Nothing Then
Sheets(aSheet(k)).Cells(rngA.Row,
[Received_Date].Column).Value = recdate.text
Exit Sub
End If
Next k
End Sub