MVC Website intermittent behavior of not reaching sometimes

I have a ASP.Net MVC Website Hosted on IIS on couple of servers with load balancers, it a very simple page when it opens it logs user details in DB and show the view.

Issue is: It becomes unreachable sometime and pages are never opened. I have to restart APP Pool to get back on track and then it happens again.

What I have tried:

1. Made sure all DB connection are properly handled, any connection that gets opened are surely closed
2. Have put Recycle of APP Pool based on volume of RAM
3. Went through IIS logs and checked that request have reached there or not
4. There are other application also running on Server but the problem is isolated to this website
5. There are global users, issue persist of different global area

What I think it can be:

1. Might be possible that Load Balancer is never diverting my request
2. My request getting lost in between networks and layer

This is Production environment and we are not facing this issue in ACC or Dev.

What else I can go ahead and check?