It’s a forum. All forums are data intensive. OK – forum plugins like bbPress may well be less data heavy but it also lacks the level of capability that comes with SP. WordPress sites are basically static by nature with very low levels of data change. Forums – especially busy ones – are dynamic with an ever changing face to the data. This is why WP-style caching can not work because the cached page is inaccurate the moment another post is made.
To perform that many queries your forum must be pumping out about 225 SQL calls every second non-stop for three days. That suggests that you have a really, really extremely permanently busy forum. And if that is truly the case then I would expect that level of activity to be on a dedicated web server. Anything less than that and you would expect bottlenecks and hosting complaints.
I don’t know what sort of hosting you are on but if you are on anything shared with that level of activity then… it is going to slow down and annoy the other websites sharing the resources.
As to what causes the high level of SQL activity… basically options, complex permissions, unnecessary plugins. It all adds up one small piece at a time. There are so many permutations it is difficult to say but as with any such software, the cleaner and leaner you run it the better the performance and resources needed.
We have users with up to 750,000 members and vast numbers of topics and posts being regularly made. Like all websites – these users need to pick their hosting with care and, as I say, when they hot a certain level of activity need dedicated hosting.