this does happen in regular hangouts if hosting the hangout from the business page. (still in Chrome) 

When I'm using the personal account, and not hosting, I don't get dropped.

I can try with a different browser at the next opportunity.

If I still get dropped I'll try clearing cache

Also, I was watching another HOA that was being hosted by a page, and noticed he got dropped in the same way (he uses IE).

I also saw the same type of drop while on when someone else started the hangout from their profile (in IE): they were dropped, and upon return there are two images of them below the main screen.  In the G+ stream, it show the person who was dropped hung out with three people (two of which are the same, the person who was dropped). This is typical of the problem with all of the drops I've observed.

Not sure if this helps. Hopefully this gets resolved before we gain viewership to our live show.

thanks!