I cannot disagree with you. Sorry she is having the issues but the fact remains HDMI is problematic on the new mini, I had it with mine.
Have you tried just turning the monitor off then back on? Also, sometimes a different HDMI cable may work better. Monoprice.com seems to have good stuff at good prices.
Hope this helps a little.
Yes, when it goes funny she has to turn it on and off again.
I've swapped 3 different cables and even loaned a spare monitor of mine - 2 days in and she had the issue reappear.
Sorry my annoyance wasn't aimed at you, but at Apple.
I've set up 3 of these new Mac Minis for customers recently - I cater to older clients and try and offer the smoothest possible experience while also being budget friendly, and to find out that a product I recommend, for reliability purposes, has an inherent problem is a kick in the guts.