There is no good reason for this, it will result in a very brittle application. It's easy for a database connection to go stale if there's a network problem or if the database doesn't respond for a little while, and with the reliance on a single existing connection there's no recovering without restarting the application.
There are other bad points to this. For instance, typically connections are synchronized so if a web application with multiple concurrent users was built this way it would limit the concurrency of the application. But the inability of your application to recover from transient problems is enough to make this worth fixing.