OK, it looks like your FlexNet Publisher Trusted Storage license cache is acting up. Although I would have expected you to receive an "Untrusted" error from FlexNet Publisher instead of that blank error.
So, it looks like you installed on March 30th. A fresh 60-day trial license activation would not have expired yet. Did you by chance have to "reinstall" from an earlier load, but not clear (i.e. deauthorize) the FNP Trusted Storage cache?
For now, have a look in the C:\Program Data\FLEXnet folder, what "Date Modifed" values are showing for the ARCGIS_xxxxxxxx_tsf.data TrustedStorage cache files, also the data_backup.00x files?
Status will tell you a bit:
if they are all missing, your FNP Trusted Storage has been corrupted.
if they have been modified since your 3/30/2012 installation/activation-Trusted Storage has been corrupted.
if they predate 3/30/2012, and yesterday by more than 60 days (i.e. you'd reinstalled) they've likely expired.
If the 60 days has expired, your trial is up. You'll need to make other arrangements with Esri.
But since you probably still have time remaining, you will need to try to "repair" the FNP Trusted Storage cache, releasing the seat locally and from the Esri Licensing Servers at Redlands.
These two Esri KB articles 38095 and 39552 have some tidbits on the mechanism. The only rub is how the 60-day trial authorization numbers are handled on Esri's license servers--the evaluation authorizations get treated a little differently for timeout, rearm and in your case repair--e.g. you won't be able to and would have to obtain a new valid evaluation authorization code from Esri.
Be sure you have an active Internet connection, and that you can access SSL/TSL services (i.e. https) from a web browser.
Then from the ArcGIS Administrator --> Desktop select the "Deauthorize" button. You should see an exchange between your system and Esri's License Servers as each component is deauthorized.
Return to the C:\Program Data\FLEXnet folder, if they are still present rename or move the ARCGIS_xxxxxxxx_tsf.data and backup files, leave the folder intact.
I'd probably reboot. Then relaunch ArcGIS Administrator and attempt to Authorize from the Desktop panel "Authorize now..." button. Work thorough the dialogs and enter the same EVAxxxxxxxxx code that you'd used before. If it runs to completion, check the Availability panel again and see if it now shows Yes for the Authorized and date values for the Expires columns--should have picked up a date 60-days from the original activation ~ 29 May 2012.
Post back if that is unclear or if you try it and are still stuck.