I think one of the problems with Chester is that so little is actually released through official channels. There's little enough good news announced on the website, let alone any bad news. The only news items on the site seem to be either promoting zoo activities or a very rare animal-related announcement. 4 or 5 news items a month just isn't enough. I'd prefer something like Edinburgh's excellent website which actually contains up to date information.
I don't know whether the lack of news is down to not having an appropriate member of staff available to post items to the site, or due to a touch of paranoia about releasing bad news, but I personally believe that a steady stream of news - good OR bad - makes people feel more involved and interested in the zoo, and makes them more likely to visit to see what's new.
I doubt I'd be as interested in many of the animals and exhibits at the zoo without Zoo Days, for example. I like to know animals' names and know a bit about their personalities and histories. I also enjoyed seeing the work that the keepers do. zoo Days did a very good job of highlighting how much thought goes into caring for the animals, and with that knowledge, you're unlikely to read about an animal's death and assume the worst (negligence or mistreatment). Without Zoo Days continuing, the website is pretty much the only channel left for this sort of information to get out.