My D5100 will constantly put the screen to sleep while I am busy using it. Is there a way to extend the amount of time the menu or preview screens will remain visible before the screen switches off?
To change the duration the screen stays on for you will need to set the time out in the menu.
Menu > Custom Settings Menu (Pencil Icon) > Auto Off Timers.
In this menu you can change the time out in seconds.
If you need the INFO overlay to stay on you can change this in the menu under "Auto image display".
Leaving the LCD screen lit longer will affect battery life, by how much is open to debate but just bare it in mind.
Source: 5100 owner with camera sitting on my lap.