File Watchdog
Log4j is able to watch the file for configuration changes. If you change the log4j file, log4j will automatically refresh the log levels according to your changes. See the documentation of .(String,long) for details. The default wait time between checks is 60 seconds. These changes would be persistent, since you directly change the configuration file on the filesystem. All you need to do is to invoke () once.
Caution: configureAndWatch method is unsafe for use in J2EE environments due to a Thread leak
JMX
Another way to set the log level (or reconfiguring in general) log4j is by using JMX. Log4j registers its loggers as JMX MBeans. Using the application servers MBeanServer consoles (or JDK's ) you can reconfigure each individual loggers. These changes are not persistent and would be reset to the config as set in the configuration file after you restart your application (server).
Self-Made
As described by Aaron, you can set the log level programmatically. You can implement it in your application in the way you would like it to happen. For example, you could have a GUI where the user or admin changes the log level and then call the setLevel() methods on the logger. Whether you persist the settings somewhere or not is up to you.