When we did this test one chromebook was the presenter and the other was a meeting attendee, the Flash player crashed on both at about the same time, but not before working for more than 5 minutes. I don't think the problem is specific to the online class provider since we were able to replicate the problem by simply setting up an Adobe Connect meeting using a free trial of Adobe Connect that Adobe was kind enough to provide for me for the purpose of troubleshooting this problem.
Both of our Chromebooks are the same model, Toshiba CB35-B3340 Chromebook 2, part # PLM02U-009008.