In particular, see the topic "Users being booted or kicked out of FlashChat" on that page, the configuration parameter autologoutAfter especially. The disconnects have several possible causes, dialup connections being a possibility mentioned (I'm guilty as charged, here; but then we're not exactly trafficking in a lot of multimedia in FlashChat). autologoutAfter defaults to a value of 60 (seconds). A suggested workaround is to bump the value up to 120. I don't know whether anyone has looked into this specific bit of configuration before - if they have, never mind; otherwise, it might be well worth investigating. It might not be a panacea, but it might just help.
-Celia