this happens, because CUDA is no longer supported by NVIDIA and therefor not included in the drivers anymore.
Which means, that if you install a new driver, the old one and CUDA are uninstalled.
NVIDIA now provides NVENC, which is faster but has fewer quality.
I was a fan of CUDA as well, but I'm using MPEG-1 instead nowadays.
Maybe there is another solution though, since I'm not an expert on this scene.
Thank you for reading my post. I hope you understand my "English".
I'm the German translator for some of Bandisoft's products and websites
(mostly Bandicut and Honeycam).