Hello Bw, and welcome to the forum! Out of context, it appears to mean "do not overlook Jeanine" or "do not let Jeanine slip through your fingers", and there are a couple of previous threads here and here. However without context (what is happening when the sentence is said or written?), the phrase "passer à coté de" is possibly ambiguous.
It's a story about a couple who are in an intense relationship as they are both working hard on their personal development. Sometimes they help each other and other times they work on things seperately.
The context of this specific sentence is when the man is writing down his thoughts:
'Je veux faire confiance. Ne pas à coté de Jeanine. Mon moment est là!'
Thanks, that definitely helps. Then on the basis of the context supplied,"do not let Jeanine slip through my fingers", assuming Jeanine is the other person in the relationship. This is reinforced by "mon moment est là!' - this is my moment!