From your question it seem like you only have one server, which begs the question "How do you test your changes?"
A better workflow would be to make the changes on your development PC and upload them to a test server first and then test the changes there. This "test server" need not be a physical server; it could be a virtual machine on your development box. The point being that changes need to be tested on some sort of webserver with the appropriate database engine or whatever your website requires. Ideally you would have some sort of automated regression and link checking etc to make sure that the changes you made did not break anything.
Once you feel happy with your changes then they would be moved to a staging site for turnover to production. The staging site should be as close to your production environment as possible. Further it should be accessible to your clients and users so that they can review and approve the changes before being placed into production.
Once everyone has had a change to review and approve the changes on the staging site the next step is to move them to the production server. Depending on the changes this might be as simple as copying files or could possibly involve schema changes to database tables etc.
The key to properly moving from the staging site to the production site is to insure:
1) You have a complete backup of the production site.
2) Have a plan to revert the changes (restore the backup files perhaps) should your changes cause a problem.
For a high volume or mission critical site you might have multiple sets of production servers with the changes moved from staging to half the servers at a time so that the website is never down. For the majority of sites scheduling 5 minutes of down time in the middle of the night to backup files and move the changes to a single production server is probably more than good enough.