Display connected via DisplayPort disconnects, reconnects when resuming, resizing windows on display

I have a new LG 29UM55 29" Ultrawide monitor, resolution of 2560 x 1080, connected via DisplayPort to my 2012 MacBook Air 13" via a Cable Matters Mini DisplayPort to DisplayPort cable that reportedly does have pin 20 wired correctly. I had previously tried connecting via HDMI, but as the manual for the display indicates, Macs are apparently unable to use the full native resolution when connected via HDMI.

A negative experience I'm having is that, when the MBA goes to sleep, the display appears to disconnect. This is noticeable only when waking it: the extra screen blanking of the display automatically reconnecting is almost imperceptible, and would otherwise be of negligible consequence, except for the result that all of my windows that were on that display are resized to fit on the MBA's built-in screen's resolution.

So, I find myself having to constantly re-maximize or rearrange windows whenever I walk away long enough for the screensaver to turn on and/or the computer goes to sleep. This is really aggravating, as I do arrange my windows quite particularly.

My options are seemingly thus:

  • Replace cable - maybe this is a manifestation of the pin 20 problem, but the display does awaken, just dis/re-connects annoyingly.
  • Replace monitor - maybe something is wrong with this unit or this model?
    • I don't have another DisplayPort monitor easily accessible, but I might be able to borrow one or at least find one I can use in a store just to demonstrate that it's a DisplayPort or OS X problem and not a unit/model problem.
  • Tweak something in OS X - maybe there's a setting that I can alter that will disable this behavior, without having to disable screensaver or sleep. Suggestions welcome!
  • Replace MBA - I'm already planning to pick up a new Macbook Pro this month, but I don't know if I'll get it in time to be within the display's return period, should I decide to return the display. I have a feeling this is not a reliable solution, because it's unlikely that the new machine wouldn't exhibit this behavior unless the behavior would change between Thunderbolt and Thunderbolt 2.
  • ??? - this is where you ingenious answerers come in.

This appears to be an issue with OSX & Windows. HDMI devices are able to be queried by the connected computer to check display resolutions even when powered off, so this is a non-issue. DisplayPort devices seem to not have this feature. When Windows & OSX wakes up from a sleep state, it checks to see if the monitor is still connected but finds the DP monitor to be in powersaving mode and cannot determine if your 2560 x 1080 desktop is still there and so resizes everything down.

Windows users appear to have a bassackwards solution:

  1. Connect monitor via DisplayPort and HDMI/DVI
  2. Configure Windows to mirror desktop on the 2 displays.