The most important trait I think for having a healthy relationship-poly or otherwise, is knowing yourself and a commitment to continuously knowing yourself.
That, combined with Marcus's sage advice to be responsible for yourself (he puts it more eloquently) makes a kick ass combination.
But-being responsible for yourself is a wasted effort if you don't take time to really know yourself.
Obviously-we don't know you.
But-let me give you an example of how I would deal if something similar happened with one of my partners.
I would take a day to myself to verify what it is I am feeling I need (and not getting).
Then I would tell my partner, look, for me to maintain a solid connection with another person, I really need at least one day a week of intimate connection for the majority of the time and some sort of conversation daily.
In our case-we've already had these discussions and agreed that this need of mine is reasonable to them.
One of them needs sex a couple times a week-that works for me.
One needs to have a kiss before bed each night-that works for me.
These types of things aren't addressing THE OTHER PERSONS OTHER PARTNER-because really-that's NOT pertinent.
It's a matter of addressing YOUR needs. If YOU need more than 1 short visit every 7-10 days; then establish-what DO you need? 5 short visits in a 7 day span? 1 long overnight? 2 overnights and 2 short visits? etc etc.
Then-without addressing the new woman-you tell said partner, look, this is what I need to feel fulfilled in a romantic relationship.
If they aren't up to that, then you back up a step (or how ever many steps necessary) to the level of intimacy you ARE comfortable having with whatever amount of time they are able to offer.
That could be friends or it could be friends with benefits or it could be go fuck yourself I never want to see your face again or whatever.
Myself-I need a certain amount of verbal or written communication (about a range of things I don't care which or what-something we are enjoying conversing about) before my libido will kick in. So, if my partner *needs* sex play from me a couple times a week, then I *need* them to commit to that minimum amount of communication.
If they can't, I can't.
One of my partners *needs* a certain amount of free time, alone time, in order to emotionally manage a large social engagement. So if we have a large social engagement that I am wanting him to attend with me, I need to be willing to give up some of our couple time so he can have some alone time to prepare for that. If I can't, he can't.
Does that make sense?
It's not about ever *making* another person do something or be something. It's about identifying what you need, and then expressing it in a way that still leaves it open for the other person to respectfully decline. In which case you accept their no.
I read a link on fb today kind of fitting to that concept... http://markmanson.net/fuck-yes
If they aren't clearly giving you the "fuck yes"-it's not worth your time or theirs to press.