Please explain why you believe it's WinSCP problem. It looks like you simply do not have permissions to edit the file. You possibly need to login with another account (or even root) to edit it.
See How do I change user after login (e.g. su root)?

I am using the AWS Lightsail, it worked well if I change the config file of nginx by using WinSCP Editor, but these day when saving the edited config file, I got permission error:

Cannot overwrite remote file '/etc/nginx/nginx.conf'.
Press 'Delete' to delete the file and create new one instead of overwriting it.
Permission denied.

So what's wrong ? How to fix it?