If you don't update your site regularly, your indexing by SE will be affected in a significant way. Google adjusts the frequency of the spider's visits based on the times you publish new contents on your site. This blog has been affected by a fluctuation in its update frequency and Google did react accordingly. Before the fluctuation, Google indexed my site contents as soon as a new post was published. Currently, it indexes my contents only after 24/32 hours. I don't know if there was also a reassessment by the end of the month that also affected the indexing routine, but I know for sure that now such indexing shows significant delays.
In a nutshell: keep a constant site update frequency without fluctuations. Be constant and regular, or your indexing will be seriously delayed or compromised.