How many days left on Terminal Services without Licensing Server

'The time limit has been over since the first client connected' is not that the grace period has ended, but that the legal use of your terminal server without having TS licenses has ended; there is no "free trial" period.

The quote from Microsoft's article makes that pretty clear.
As far as the remaining grace period is concerned, you can try to check the date of the %Systemroot%\System32\Lserver folder on the TS license server; this should be the date you installed the TS licensing.

You could try lsreport.exe from the Resource Kit as described here:HOW TO: Use the Terminal Services Licensing Reporter Tool (Lsreport.exe)http://support.microsoft.com/?kbid=317592

Don't forget that the licensing server might have a grace period of 120 days, but the temporary licenses it's issuing are only valid for 90 days; from then on, the client will require a valid license to connect.