..m my left menu page refreshing and menu going to disappear.
It's little hard on exactly suggest best way of implementing it but surely you can achieve what you need using one of the state management techniques.
Have a look at these:
MSDN: ASP.NET State Management Overview
State management in ASP.NET - 1
ASP.Net State Management Techniques - 2
For example, in your case, you can keep one hidden field
as a flag if the left nav bar is visible or not. Once you click top horizontal menu, based on which left nav bar appears, set the flag (lets say it isLeftNavOpen) as true. Now, always in your code during page load, check if the flag is true, if so, set the visibility of the left nav as visible.