The first time I read about local volatility, implied volatility turned out to be the average volatility from today to the option's expiry date.
Let we have two Call options, $C_1$ and $C_2$, expiring on $T_1 = 15$ days and $T_2 = 45$ days and we extract the implied volatilities: $\sigma_1 = 40\%$ and $\sigma_2 = 30\%$, the term structure exhibits backwardation. Moreover, I add another hypothesis: the implied volatility is the perfect forecast of the realized volatility, so no way to make (or lose) money by hedging the Delta because the underlying will be as much volatile as the implied volatility says.
Now I buy a Delta neutral $C_2$ ($= C_2 - \Delta$ stocks): I'm paying $\sigma_2 = 30\%$ to enter this position that will last $45$ days over which I will see average volatility equal to $30\%$. However, $\sigma_1 = 40\%$, so it will happen that the underlying will be more volatile during the first $15$ days than during the following $30$ ($= 45 - 15$) days (of course, we could talk about forward implied volatility but that wouldn't add much content here).
My question is: given that the underlying is much more volatile during the first $15$ days and I'm paying lower average volatility ($\sigma_2 < \sigma_1$), what does stop me from making money by systematically closing this trade within $15$ days if the implied volatility term structure keeps being in backwardation and the other hypothesis hold true?