Since installing the iLLM I've had fairly regular trouble. It looks very useful, but getting it to do what it's supposed to do isn't always a breeze. I've already lost a couple of days to tracking down problems on the iLLM. Thank you, Pace. (end of sarcasm)
My main iLok quit working, but strangely the light remained lit, and the iLLM still recognized all my licenses. But Altiverb, Ivory, and all my other apps and plugins that depend on iLok simply refused to recognize that the licenses were there. I spent many hours eliminating possible causes, making sure that it wasn't an OSX version problem, or a dysfunctional plugin or app. I was about to pull the lever and instigate the Zero Down Time option. However, before I could do so, I found a little trick that I had not seen before.
Ok, let's cut to the chase. You've got an iLok that lights up and is recognized by the iLLM, but not by any of your software that depends on the iLok. What's happened is that it has gotten "out of sync."
To get it back in sync, open up your iLLM app, click on the affected iLok in the list on the left, then click "Show Details" over on the right hand side. There will be some items to click which include "Sync/Repair." ———————v

Click Sync/Repair and let it do its thing. When it's done, chances are your iLok will now work.
If it doesn't work at this point, and if you're sure you have the latest versions of everything, you probably should invoke ZDT and get some temporary licenses on your spare iLok so that you can get back to work, because that iLok is probably broken.
Shooshie
PS: I'm purposely putting this in a DP forum, rather than a hardware forum, because this directly affects DP users, and I want it to be seen by all who read the DP forums.