The auto connect code is unlikely to be a culprit here; they hinted at, then jjust outright confirmed that it's a lack of server resources issue.
I don't see any confirmation that the auto-connect code, which is standard fair these days, is overly aggressive to be on it's own causing a problem.
They need more servers according to their own admission, and the rather obvious state of the situation. The fact they couldn't immediately respond indicates they aren't hosted on a dynamic cloud. Or at least not one with any more room lol. The fact that lots of people are also causing "Please sir, may I have some Session?" is never going to make a full server very happy, but the fact they are claiming sessions are fine for those actually connected leads me to believe they are gracefully handling the requests... it's just.. too much.