Bad Solder
The solder is the light metal that holds the electronic connections together within the console. If the system overheats, the solder may crack and sever many of those connections, causing an eventual system crash.
Dust
Old consoles tend to get dirty, and the NES is no exception. Unless your console is frequently taken apart and cleaned, dust and other particles may accumulate inside, blocking various connections or catching fire and burning wires.
Power Adapter
The power adapter for the Nintendo may become loose after several decades of use. If this happens during game play, the console will suddenly lose power and seize up. If a short occurs in the old power adapter wire, you may want to replace it, as it will continue to crash your system.
Broken Games
NES game cartridges are generally considered tough. However, if these cartridges are damaged in any way, or the internal components are busted or dirty, the console will fail in reading the game's code and seize up.