LogWatch runs once per day, from cron -- If you want more frequent notifications you can run LogWatch more frequently, but that this will send you everything that LogWatch normally complains about.
If you want to watch for specific messages you should be using something more sophisticated than LogWatch (
syslog-ng with custom filters/actions springs immediately to mind, particularly if you want "immediate" notifications), or writing your own tool to scan the log files on a tighter schedule.
Be Careful What You Wish For
Asking your system to send you emails for every "important" event can quickly become overwhelming. For example there are over 1000 failed login attempts on my personal system TODAY (in the past 11 hours) -- I certainly don't want to be emailed for each one of those: I have enough spam.
Proper monitoring and alerting should only be telling you about things that require action on your part (LogWatch in my experience is awful at that, to the point where I've completely disabled it in my environment because it's just creating noise) -- Make sure whatever system you implement has a very low noise level so you don't fall into the all-too-common trap of ignoring alerts because "I see that all the time and it's never important".