As mentioned, all GUIs (including menus) are either real-time or event-based. For event-based menus, you use a GUI toolkit like Win32, Qt, or another.Actually, I do know how to make a menu. This question is for a real time rendering menu...
For real-time menus (like what 99.9% of games require), you make them yourself and treat them similar to any other game object in your game.
I suspect you are accidentally drawing your menus outside your rendering loop, so they don't get redrawn.
This is probably a communication issue because of different lingo we are using. Why don't you post an example of your working, non-realtime, code, and we'll tell you where to go from there? We might not all speak using the same terminology, but we all speak computer code.
What language are you using? Our answer will change depending on your chosen language. What APIs/third-party-libraries are you using to draw graphics on-screen? Our answer will also change depending on that.
Finally, what is a small working example of your existing non-realtime menu? We don't need an entire project, just the main loop and the functions involving the menu. We want to help you, but sometimes it's a bit difficult for us to understand someone's problem without seeing at least part of their code.