Zulip. It's Open Source, you can either pay to have it hosted or host it yourself, it has mobile apps and a web interface, it has a good API for integrations, and the conversation model feels great.
This has been a problem ever since email: many people reply to the last mail they have from a list, sometimes changing the subject, and then get surprised when the mail is threaded under the mail they replied to.
I've seen this occasionally on Zulip instances, but a reminder and a suggestion that the topics are like email thread subjects or forum thread subjects tends to help.
Given that you mention a big public server, it's likely caused by an issue specifically related to that server's scale/usage patterns, and I'd like to make sure we investigate it.