I conducted a little experiment. So, I managed to get the Google spiders to the point where it was indexing four to five pages per hour. It was really consistent, too. Happened all day and every day. I then stopped posting new content on my home page. After a week, the spiders stopped coming back. So, the lesson here is that you should always have fresh content at least once a week. We have to train the spiders to keep coming back. In order to do that, it needs something new to see.
Anecdotally, I would tend to agree. I've been working for a couple of months on getting my website shifted over to some new software. So I haven't been feeding fresh stuff to the spiders. I have noticed my traffic drifting down a bit during those two months. It could be something else, but I suspect it's my inactivity.
Yes its true that spiders crawl your website late when you stop updating your website. But it doesn't effect too much in ranking.
I think having new content does effect rankings. I have noticed that when I havent added any pages to my site for a couple weeks my traffic tends to drop...
Started updating more frequently again, and the spiders are back at the previous pace once more. Google is indexing five new pages an hour again.