It is "make it happen" because "make" is a causative verb. After "make" you must use an object and the base form of the verb. The teacher made us do our homework. There is a long explanation for other causative verbs in both active and passive. I can explain it if you have time, but that is the basic answer for your question.

Somebody asked a related question a few hours ago, and was lucky enough to get the wonderful Peachey as their answerer. Take a look at this: http://www.italki.com/question/261397

Here is the exact structure of this rule-- make + noun /pronoun / other things + verb (present participle)