The game client encountered an unexpected error and had to close.

[VegaNovus]

Next time it stops working do these steps.

Press Windows + R
Type eventvwr expand Windows logs and then select Application

Look for any errors that relate to FFXIV:ARR
If none appear, try System logs and looks for any errors there.

Post the errors here and I'll try give you a solution.

[RestlessHero]

The one I see that keeps popping up says
"Faulting application name: ffxiv.exe, version: 1.0.0.0, time stamp: 0x521be282
Faulting module name: nvumdshim.dll, version: 9.18.13.1144, time stamp: 0x51414e1a
Exception code: 0xc0000005"