But when you want to say "many times"...
... it's time to use another "time" word! We use the word "פעם" in this case - it can also be translated as "once" sometimes. My best tip is - זמן is a general word, פעם is more similar to "occasion."
I saw this movie many times - רָאִיתִי אֶת הַסֶּרֶט הָזָה הַרְבֵּה פְּעָמִים
This time I can't help you - הַפַּעַם אֲנִי לֹא יְכוֹלָה לַעֲזֹר לְךָ
Each time I see him I am happy - כָּל פַּעַם שֶׁאֲנִי רוֹאֶה אוֹתוֹ אֲנִי שְׂמֵחָה
Well, this is how it works... "Ehm, kind of late now, it's time to finish this newsletter and send it out... and what time is it now, by the way?" I am thinking.