I've had an issue with some 2014 SP2 SQL servers, where multiple instances stop responding and have to be restarted before the applications can reconnect to them.
It's standalone instances, all on the same server. Databases are on local store.
It seems like the problem comes from SQL server spiking up CPU usage (each instance is using 3-5% CPU non-stop). Here's what is odd... if I reboot the server it's <3% CPU usage average. But if I restore a database into any one of those instances the server starts going CPU crazy after about an hour. If I never restore a database, never a problem.
After the CPU starts going crazy, if I look at execution plans on all instances, the statistics are WAY off. (expected 82 rows actual 22500) Statistics look fine before issue starts.
How many SQL Server instances do you have installed? Can you list their version and edition?
Did you configure for each of those SQL Server instances the min and max memory? If so, post here their memory configurations as well.