1st , contrary to what has been suggested before, buying a D_DVI cable won't solve anything that couldn't be solved by buying a single-DVI cable as the 2nd DVI isn't even connected on the MacMini (or any other GFX-card
2nd 1920x1200@60Hz is the absolute maximum a single link DVI can do, so problems with signal losses are to be expected.
3rd the DVI-part of the Mini is prone to complete failure (leaving you with only VGA) but sofar I haven't heard of this bug sneaking up but allways going from 100% working to total failure in an instant.
What you could try:
- Use other adaptor/cable
- reduce used bandwitdh by going a lower res.
I'm also not sure, what your actual setup is.... you write HDMI which suggests a TV, but those are all 16:9 not 16:10 implying 1920x1080 as optimal res.
If it is an actual 16:10 monitor, doesn't it have a DVI input you might want to try (eliminating the need for an adaptor ?