The short answer: Your observation is caused by some sort of central limit theorem.
The long answer: The reason for the volatility smile/skew is the non-normality of the assumed return distribution. If the implied volatility of out-of-the-money put options is higher than of at-the-money put options, it implies that the market assumes that the risk-neutral probability of a downside return is higher than implied by a normal distribution. The implied volatility surface can therefore be seen as a convenient way to describe the underlying risk-neutral return distribution.
Let's assume that the true underlying process generates daily log-returns which are left-skewed and leptokurtic, i.e. downside moves are larger than upside moves. If we observe options with a maturity of one day, we will find that the risk-neutral distribution corresponds to the skewness and kurtosis of the underlying return process. However, if we extend the time horizon returns are aggregated and the central limit theorem starts to work. Thus, longer return horizons generate more normal returns. So for example, if we observe the volatility smile of thirty day options we observe the assumed risk-neutral return distribution of the 30 day log-return which is the sum of the next 22 or so log-returns. Therefore, the 30 day return is necessarily less non-normal than a one day return. If we switch back to the corresponding volatility surface, less non-normal returns imply a flatter smile.
In reality this is a common observation of implied volatility smiles and of historical return distributions. If you calculate the skewness and kurtosis of daily, monthly, quarterly and yearly returns you usually find that yearly returns are the least non-normal. The speed of convergence is dependent on the initial non-normality of the process and for highly non-normal distributions convergence can be very slow.
This answer corresponds the answer of Quantuple who named important microstructural and hedging arguments.