You are not necessarily doing anything wrong. Imagine there is actual autocorrelation at lags 1 and 12. You find it with LB(1). You still find it with LB(2) and LB(3), but the results are less strong as the test statistic gets diluted by the non-autocorrelated lags 2 and 3. When they get diluted further, the results become insignificant (lags 4 to 11). But then you reach lag 12, and the autocorrelation at lags 1 and 12 are now strong enough so as not to get diluted to the level of insignificance in LB(12). So you get a significant result there and similarly for 13.

This is just one example. You could come up with something similar with other combinations of autocorrelated and non-autocorrelated lags.

You are not necessarily doing anything wrong. Imagine there is actual autocorrelation at lags 1 and 12. You find it with LB(1). You still find it with LB(2) and LB(3), but the results are less strong as the test statistic gets diluted by the non-autocorrelated lags 2 and 3. When they get diluted further, the results become insignificant (lags 4 to 11). But then you reach lag 12, the autocorrelation at lags 1 and 12 are again strong enough so as not to get diluted to the level of insignificance in LB(12). So you get a significant result there and similarly for LB(13).

This is just one example. You could come up with something similar with other combinations of autocorrelated and non-autocorrelated lags.