Right. No one (except the Google guys who work on the algos) can really connect the two. But 'user experience' and 'overall quality' of the website are two important factors in Google deciding website's ranking in searches. I believe the the sudden rise of the broken links on the site led to Googlebot thinking that the site offers a bad user experience and not decided to rank the website lower.
Of course, this is just a guess. I've checked and checked and re-checked whether we're doing anything that's against Google TOS and could not find anything that requires attention.
The 'experts' told me to 'remove' the content generated by users that is 'thin'. Given that our site has over 50k discussions, it's totally impossible for me to visit every discussion and remove the content that 'I think' is low value.
Now, you're experiencing the similar trend in rise of crawl errors and drop in traffic+crawl rate. Our website never got hit by Panda or Penguin because we never were a content farm or implemented any black-hat SEO stuff.
The only thing I'm interested in knowing now is how long will Google take to restore the rankings when the error count drops below the acceptable level. Some of the webmasters of smaller websites have said that the rankings & traffic restored almost immediately. I'd have loved to have more opinions/experiences on this.
Right now I'm going to just wait and watch what happens when the crawl errors drop below 3k-5k and whether that affects our traffic - I 'think' it will take at least a week or two to 'restore'.