Is it possible to implement a login system that protects against this scenario, while still allowing your user the convenience of "Remember this computer for 30 days"?
No. To put it bluntly, it is impossible. That will be a huge, complicated and simply a non feasible task for an authentication system to fulfill.
All what you can do is to be careful of the vulnerabilities that may your software, operating system and network settings suffer from, and think how to protect yourself from eventual vulnerabilities and mitigate the threats on different levels of the layered security mechanism.:
