I also have an Asus Xonar DG, however I do not run Windows 7, I run Windows XP 32-bit.
If I "testplay" the sound (mIRC Options -> Sounds -> toggle through the audio options to have "Beep" selected -> check the "Use internal beep" checkbox -> push play), I have no problem hearing the beep repeated 5 times with a delay of 100 (stock defaults).
However, I will point out that if this does use MME, this
wouldn't be the first time I've heard of problems with Asus's drivers and MME support.
For the issue I experienced above, I believe the problem may have been -- but not 100% sure -- that I had disabled the Cmaudio8788 (RunDll32 cmicnfgp.cpl,CMICtrlWnd) and Cmaudio8788GX (C:\WINDOWS\system\HsMgr.exe Envoke) startup tasks in the registry associated with the Xonar DG drivers (I'm OCD over unnecessary things needing to be run on log in). So if you too have done that, re-enabling them might be a wise choice to see if things improve.
My aforementioned experience, combined with this thread, leads me to believe that the Internet's claim of the Asus Xonar series having "awesome drivers" is utter nonsense -- which is what I've come to expect from hardware review sites the days.
However, I will happily state that the DirectSound support in the XG drivers is quite good (I've yet to find any problems with those), so possibly mIRC making the move to DirectSound -- especially given that Windows 9x support was officially removed from mIRC long ago -- would be a better overall choice here.
I'm not saying "hey Khaled, go do a bunch of work due to Asus' wonky drivers!", but the reality is that vendors tend to focus on DirectSound these days, and most of us try very hard to avoid companies like Creative Labs (horrible quality) or Realtek (other driver wonkiness or missing features we want). There are probably some simple, and license-free audio playback libraries that use DirectSound which could be dropped in for MME replacement as well.
My $0.02.
