Armin, thank you very much! This is indeed what is happening.
The presence of a shortcode module (even with my shortcode plugin deactivated) will cause the page to refresh upon resizing the browser window to mobile/desktop width.
Could it be that there is some issue with the coded used? I managed to upload a file using the mpeg4 codec instead of the h.264 (x264) codec and had no issues.. the file was 21 mb in size.