MacOS – dual screen resolution setting is reset after logout, reboot or sleep

This was eligible for me: edit /Library/Preferences/SystemConfiguration/com.apple.Boot.plist like this:

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
    <key>Kernel Flags</key>
    <string>darkwake=0</string>
</dict>
</plist>

and restart your mac. Mountain Lion forces me to enter password twice but it wakes up and works.

Try resetting the NVRAM / PRAM as noted About NVRAM and PRAM

Resetting NVRAM / PRAM

1. Shut down your Mac.
2. Locate the following keys on the keyboard: Command (⌘), Option, P, and R. You will need to hold these keys down simultaneously in step 4.
3. Turn on the computer.
4. Press and hold the Command-Option-P-R keys before the gray screen appears. Hold the keys down until the computer restarts and you hear the startup sound for the second time.
5. Release the keys.

See if the sleep problem still occurs, if it does try resetting the SMC as noted Intel-based Macs: Resetting the System Management Controller (SMC).

Resetting the SMC for Mac Pro, Intel-based iMac, Intel-based Mac mini, or Intel-based Xserve

1. Shut down the computer.
2. Unplug the computer's power cord.
3. Wait fifteen seconds.
4. Attach the computer's power cord.
5. Wait five seconds, then press the power button to turn on the computer.

If the problem still persists and you are running OS X Mountain Lion version 10.8.2, there may be a sleep bug that is effecting the reliability of sleep on a lot of Macs as discussed Problem with waking from sleep with 10.8.2

My Mac Pro (early 2009 2.66 GHz Quad-Core Intel Xeon) won't wake from deep sleep after installing OS X 10.8.2 . I have the default setting set for sleep. The only way to "wake" the machine is to hold the power button down to shut down and then restart. I've reset NVRAM (pram) and tried removing power cable. Nothing helps.

Since your Mac Mini is very new I would also consider contacting Apple Support and see what they offer as a solution and at the least notify them of the issue, I am sure they are working on a fix probably scheduled to be included with the next OS X update.