I've noticed that this issue occurs when the nvidia driver has been updated. Attempting to start kitty will result in a message like this in dmesg:
[183910.448118] NVRM: API mismatch: the client has the version 460.39, but NVRM: this kernel module has the version 460.32.03. Please NVRM: make sure that this kernel module and all NVIDIA driver NVRM: components have the same version. At the moment the only option seems to be to avoid nvidia-driver updates unless I'm ready to reboot, which is probably not a bad idea anyway.