I guess that would depend on the partner? And what do you mean by vulnerability in that context that would make her lose respect?

And what do you mean by wrong times or reasons?

Most people seek emotional support, resilience and trustworthiness from their partner, and being excessively "vulnerable" can definitely hinder you from playing that role effectively. This is what can sometimes be experienced as a loss of respect. What you really want is to show a mere modicum of emotional vulnerability that your partner can then have some opportunity to empathize with, and not view you as overly brittle. But not more than that.

What could be examples of excessive vulnerability?

Why would I seek emotional support from someone so disconnected from their emotions they can't show more than a "modicum" of vulnerability?

How could I trust someone's resilience when they don't show they've been through things that built that resilience, and demonstrate it?

How can I trust someone who so closely monitors how much and what sort of emotions to show to me?

Why are you assuming that someone who sensibly refrains from overly impulsive behavior wrt. showing their emotions (this is what "self-monitoring" ultimately means: we all do it in all sorts of social contexts, and it's a normal part of being a healthy, well-adjusted person) must necessarily be "disconnecting" from them altogether and lacking in emotional resilience?

If you manage to "self-monitor" all the time, and never show more than a modicum of vulnerability, that seems very disconnected to me.

Perhaps 'disconnected' is the wrong word, but what I mean is that emotionally healthy people feel their emotions and express them, not just hold them at arm's length and pick and choose which to feel and express.