I don’t think unless your GPU is defective you should not have to replace it, My friends plays Rust with a GTX 260 max core just fine.
Things that could cause your issue
Incorrect memory timings or voltages
Corrupt driver install
Unstable overclocks (GPU or CPU)
Incorrect MB voltages (generally NB/SB)
Faulty graphics card
A badly written driver or piece of software, but this is an unlikely cause in most cases
[editline]13th January 2014[/editline]
Also you can try
Turn computer off unplug power cord.
Remove your GPU from your computer, turn the computer back on uninstall all Nvidia drivers. Turn the computer off and reinstall the GPU make sure all power connections are nice and tight and the GPU is installed all the way into the pci slot.
Turn computer back on and windows will install a driver. Try to run Rust if still crashes install latest NVIDIA driver. Also make sure you installed chipset drivers for your motherboard after you reinstalled windows.