I had this issue after updating an EDN license recently - hope this helps someone avoid the same frustration and save some time.

The Problem: 

After updating an EDN subscription in ArcGIS Administrator then opening an existing Visual Studio solution that uses ArcEngine components the following message appears after a few minutes:

When you click on the OK button the ESRI licensing code kills the Visual Studio process with no warnings and no option to save changes – very annoying if you are in the middle of writing code.

After a bit of searching I noticed that the old authorizations are still listed in the ArcGIS Administrator > Engine > Availability list. Surely the ArcEngine licensing code would ignore expired licenses and just check for current ones? – Apparently not.

The Solution:

To fix this issue go to the ArcGIS Administrator > Support Operations and click on Deauthorize. Select the expired licenses and click next . After removing the expired licenses I haven’t seen the ArcGIS Engine licensing issue in Visual Studio.