SQL server is getting stuck all of a sudden
Try running sp_Blitz, a free health check for your SQL Server (disclaimer - I'm the author).  You can also run it with @OutputType = 'markdown' if you want to share the results here at Stack.

I've got a hunch that you're running into THREADPOOL waits, and sp_Blitz alerts about that. THREADPOOL means your SQL Server ran out of worker threads to service incoming queries. It won't show up in the OS or SQL Server error logs.

When it's happening, you'll be able to connect to SQL Server using the Dedicated Admin Connection (DAC) (disclaimer: that's a blog post on my site.) The DAC is a set-aside CPU scheduler used just for emergency troubleshooting. From there, you'll be able to see which queries are burning up all the worker threads - typically it's a blocking problem.