Like expired milk, and old Google cache date won't hurt you. Well, at least expired milk according to Adam Conover won't hurt you. And at least according to Google's John Mueller, Danny Sullivan, Martin Splitt and others - an old cache date won't hurt your Google rankings.
We covered this about a month ago already - where Google said don't worry about the cache date being a month old. So yes, the cache date has updated but it is still a month old for many including this site. But no, it doesn't impact this site's rankings or indexing, nor should it impact your site's rankings or indexing in Google.
John Mueller from Google just said on Twitter "The cached page is not always representative of crawling & indexing, so I generally wouldn't use the date shown there as a sign of a problem." Danny Sullivan said on Twitter "Yes, I'll pass this on. But please keep in mind that the cache date does not reflect the current date of a document indexed in our systems." Martin Splitt said in Friday's webmaster hangout at the 23:33 mark "I am quite surprised how many people asked about cache. Cache is like a nice convenient feature that we offer but it is not related to indexing."
Still, this is concerning for some SEOs and I suspect sooner than later Google will update the date to be more recent.
Until then, don't blame your cache date for your ranking issues in Google.