I do not have a definitive answer but I strongly suspect that the Is Dirty flag that signals a formula to be recalculated was dropped somehow. Since simple SUM(...) and this+that formulas are not volatile (i.e. recalculated for every calculation cycle in the workbook) they would only be recalculated if reasserted.
Solution: use Find & Replace to globally search for = (the equals sign) and replace it with = (the same thing). This essentially rewrites every formula in the worksheet thus resetting the cell's Is Dirty flag. I've tested your worksheet this way and it seems to correct the errant behavior even after saving, closing and reopening.
Sorry if I cannot be more specific but without knowing the complete history of the workbook/worksheet I can only pass along what I've found to correct the problem without completely understanding the problem itself.