After reading a lot of threads from users having a very similar issue and also noticing that Dell is not responsive to those threads, I'm not holding out much hope here to get my issue resolved but here goes anyway...

I purchased TWO E2311H monitors in December 2012.  They are connected to a HP Advanced Dock via the DVI ports.  For SIX months, these monitors have operated flawlessly.  When the computer goes into SLEEP mode, my monitors would wake up, as expected, when I returned to the computer and moved the mouse or pressed a key on the keyboard.

However, about three weeks ago, all that stopped working.  First, I noticed a pop-up message, "softOSD Local Command Processor has stopped working" and since then, neither monitor will wake up when the computer comes out of sleep mode.  I found that the above message is used by OEMs for their peripheral devices.

I have two workarounds:  (1) If I remember to Power off each monitor before the computer goes to sleep, I can simply Power On the monitors when I come back to the computer, or (2) if the power was left on, I can unplug the power cord from each monitor and plug it back in again.

If I don't perform the two workaround steps above, nothing else works except rebooting my computer.  When the amber light is on, nothing on the monitors work...not even the power switch.

Also, I have the exact same HP Advanced Dock in my office with the same monitor configuration (EXCEPT the two monitors are NOT Dell monitors).  When my computer goes into SLEEP mode at my office, my monitors there have no problem waking up.  Appears to be a Dell issue that Dell is not willing to address.