How do I restart a total if a cell equals 0?

I am trying to automatically reset my total if a cell equals 0.

A1 9
B1 9
C1 0  <-- Reset total
D1 9
E1 9
F1 9
G1 9
H1 36 (Should = 36, resetting at any cell showing 0 and not show 54) 

Fields A1:G1 hold the daily hours worked on the roster, while H1 contains the total hours worked that week. (However, I want to reset this total if there is a 0 hour rest day)

Is there a formula that can do this?

We can use a "helper" row. In A2 enter: =A1 in B2 enter:

=IF(B1=0,0,B1+A2)

and copy across. Finally in H1 enter: =G2

Wih BVA / Macros

Public Function sumreset(dataRange As Range)
    totalSum = 0
    totalLength = -1
    indicator = "none"
    totalLengthRows = dataRange.Rows.Count
    totalLengthCols = dataRange.Columns.Count
    If (totalLengthRows = 1) And (totalLengthCols > 1) Then
        totalLength = totalLengthCols
        indicator = "cols"
    ElseIf (totalLengthRows > 1) And (totalLengthCols = 1) Then
        totalLength = totalLengthRows
        indicator = "rows"
    End If
    For i = totalLength To 1 Step -1
        Select Case indicator
            Case "rows"
                nextData = dataRange(i, 1)
            Case "cols"
                nextData = dataRange(1, i)
        End Select
        If nextData <> 0 Then
            totalSum = totalSum + nextData
        Else
            i = 1
        End If
    Next i
    sumreset = totalSum
End Function

Open VBA / Macros with ALT+F11, under ThisWorkbook insert a module and paste this code on the right side.

On cell H1 put =sumreset($A$1:$G$1) and that's all.