It sounds like you are talking about a MILD induction. No, it is not necessary to keep repeating your mantra until you fall asleep. You only need to repeat it until your intention is set. By my definition that means until you can repeat the mantra over several times without other thoughts distracting you. Then you can just let go of the thought and fall a sleep.
You can find some information on meditation:
meditationand How do you meditate
Meditation or relaxation might help you get to sleep more easily. What you would do is: first use meditation to get into deep relaxation then do your MILD mantra the let go and allow yourself to fall asleep.