The majority of relationships that break up are monogamous ones. But no one says when a monogamous couple breaks up that it was "because of monogamy" but they presume that if a poly person breaks up with their partner or partners that it must be because it was poly? In DA:O you can break up with characters and you can break up several times... one of the reasons why it occurs is because you are forced to choose one person over another. Knowing there are feelings you have for someone, which may represent an important part of you that you can't act on because you are with someone else leads to cheating and breaking up all the time in mono relationships. Most TV soap operas have this occur... because it is so common. I have seen poly relationships work and not work... I have seen mono relationships work and not work... It would be pretty rich for me to claim that it is inherent in either to succeed or fail when both occurs.
Of course most relationships that fail are monogamous. This is because most relationships throughout modern(and sometimes even ancient) history are monogamous(or at least supposed to be). We humans(both male and female) tend to be pretty territorial over who we sleep with. Monogamy is an effective way to combat this territorial behavior, marriage even moreso. So when cheating occurs, the breakdown of the relationship can quickly follow. But this is not the only reason for a relationship failing, and many times there is a litany of symptoms of a poor relationship that can actually lead up to cheating. There's anger, there is neglect, there is stress, there is sickness/health issues, there is money. These are only some causes.
When two people get together, any one of these things can cause the breakdown relationship to fail, and when combined with one another they can cause a great deal of social and emotional destruction. This is the risk you take when getting involved with another person. It's part of the reason marriage exists. It's is to make it harder for your partner to just up and quit. It is a social and cultural incentive to work through the problems in your relationship rather than just run away because they are too hard to deal with. The social stigma of divorce, though less harsh than it was in years past, is still substantial enough to give a person pause before dumping their partner because they just don't want to deal with them anymore.
Monogamy is not easy. In fact, it's incredibly difficult. A committed relationship, in my opinion, is the most rewarding challenges anyone can ever attempt. But invariably the hardest. I admire a moderately happy 30-year marriage more than I do a Super Bowl ring, or the climbing of Mount Everest. The dedication and hard work that goes into a relationship like that can take everything you have mentally, emotionally, physically and spiritually.
So why, in the name of all that is holy, would you want to double up on that kind of challenge? When you do this, you are increasing the chances for a great deal of hurt and anger. No matter how open a relationship is, you're still going to get hurt if your 'partner' wants to spend Christmas Eve with his/heryour other 'partner'. Or he/she takes him/her out to dinner one night, even if it's the only night you're off of work the whole week. Or if on a night you're feeling really horny, he/she decides to visit his/her other, other half.
When you have feelings for someone you're not in a relationship with, it is a test of your relationship. It is a test to see if you really love the person enough not to act on them. It is a test to see if you are truly committed to making what you already have work. Failing that test speaks a great deal about the strength of your relationship. So having a relationship with multiple people, where all parties are aware of what is going on, in my opinion is a weak relationship from the start. At least one party has already admitted that they do not wish to confine their affections to one person, no matter how deserving that one person is of their love and devotion. No matter how much he/she deserves to have that kind of loyalty.
THAT is why every polygamous relationship I have personally observed has failed. There's been a propensity of one party feel like they are a third wheel, left out or simply ignored over the favoring of another part of the relationship. So they stray out to someone else more willing to give them the attention they feel they deserve. Or they strike out at another member over what amounts to children fighting over a toy.
Now let me be clear: I'm not here to judge you, or your relationship with your significant other(s). I don't know you, I don't know who you are with or what they are like. It isn't my place to say anything about what your relationship is like.
But in my opinion, polygamist relationships are weak by the very nature, and do not work in the long run. Again, this is based on what I've seen. I have seen monogamist relationships break down, just as you have. But I've yet to see the love, dedication and devotion of the many long-lasting monogamous relationships I've seen be equaled by those with more than two people. And I highly doubt I never will.
This is why I disagree with this kind of relationship being accepted as normal, it is why I highly doubt any culture will accept the normalcy of a long-lasting, committed polygamous relationship. It is also why I don't think Bioware will be able, or willing, to portray one in their games. The story and characterization loops they would have to jump through to make it believable, along with the practical problems with implementing it within the gaming system itself, makes it a high-cost, little-reward feature they are unlikely to put in.
I've heard it said that humans are not naturally monogamous creatures. We don't find one partner and stick with them for the rest of our lives. We go through changes throughout our lives and seek out partners who fit with where we are at any given point; and it's these connections which help us grow and allow us to continue to change. And I'm inclined to agree with that. If it so happens that at one point in time you develop a close, intimate relationship with a couple, as opposed to a solitary person, then so be it.

That kind of life has no appeal to me personally. I can understand why it appeals to others, but to me it is a very lonely way to go through life. I want my wife to know who I was ten/twenty/thirty/fifty years ago, and I want to know what she was like. I want to see the changes in her, and I want her to see the changes in me. Every wrinkle, every slowed step, every changed political opinion, everything. My (very wise)mother once asked my sister when she and her husband were having relationship issues, "Hon, do you want to be married to the version of *Jim* you married twelve years ago?" My sister's response, after a moment of thought, "No! I want MY *Jim*!". It made my sister realize that all the changes her husband had gone through, the very things that she was complaining about, were changes she had gone through with him. And she was not the woman he had married twelve years ago, either. So they fell in love all over again, with all of their shared faults and flaws.
That's the kind of relationship that I want.
And the majority of relationships that succeed are monogamous ones.
Also this. Very much this.