It feels like either a DB issue (but I don't know if you have separate DBs for each forum or not - if not, then it's not a DB issue, probably), or a caching/proxy issue (I don't know if you use external services like Cloudflare, for example).
It's not quite random, but it doesn't seem to matter about site traffic (being in Australia, I'm often on when relatively few people are showing as being on). I had one instance of it telling me I couldn't post within 30 seconds (or was it 60?) of a previous post even though I hadn't previous posted that day. When I checked by opening the forum in another tab, the post had gone through.
I agree with others who've said that once you post you often can then post without delay for a while. That feels like a DB issue relating to a server either waking up that DB from disk or caching it locally (as opposed to a general network caching or proxy issue).