There's a limit of 64 sortfields to a sort which is one of several reasons why you might get that error (you're trying to create 365 sortfields). I've guessed at what you want to do and tidied your code to the below. If it's not what you want please can you describe in simple words what you want your code to do?
Code:
Sub SortDaysProvider()
Dim DayRange As Long
Dim TopRow As Long
Dim sRange As Range
Dim fRange As Range
Application.ScreenUpdating = False
For DayRange = 1 To 365
TopRow = (DayRange * 17) + 9
With ActiveWorkbook.Worksheets("Input Calendar (2012)")
Set sRange = .Range("E" & TopRow & ":" & "BN" & TopRow + 14)
Set fRange = .Range("E" & TopRow & ":" & "E" & TopRow + 14)
With .Sort
.SortFields.Add _
Key:=fRange, _
SortOn:=xlSortOnValues, _
Order:=xlAscending, _
DataOption:=xlSortNormal
.SetRange sRange
.Header = xlGuess
.MatchCase = False
.Orientation = xlTopToBottom
.SortMethod = xlPinYin
.Apply
.SortFields.Clear
End With
End With
Next DayRange
Application.ScreenUpdating = True
End Sub