Edit: While writing this, all of those great responses popped up (I'm quite slow), which are all far better than what I came up with. I believe I missed the mark a bit and must have avoided all that media you guys are talking about. Lucky me? I will still post this, since I put effort into it - just note that I agree with everything mentioned before me and that I don't intend on excusing abusive relationships.
Falling madly in love has something obsessive and crazy about it - I guess that's why we say "madly".
Many things we do when falling in love can seem insane to an outsider. Some may write the name of their crush 300 times into their diary, secretly hope the crush's GF/BF gets a really bad cold (or worse), follow them around just to see their face for a few minutes per day. I could continue this list on and on, with everything sounding more and more crazy if you think about it.
Yet most of us who have crushed really badly, especially when young, may have done one or the other on that list. So we can relate to a character who does something similar, even if the actions taken really aren't the most grown up way to handle 'falling in love'.
Luckily, most of us grow out of that phase without it ever being something to worry about. Some don't however - and those of us who have experienced abuse or stalking can be quite sensitive when media portraits that behavior as something one doesn't have to worry about. With the majority of victims being female, I'm not surprised that especially male characters come under scrutiny the most.
We also can't forget that relationships are messy. Control issues, arguments, distrust, those are the ugly sides of partnerships that even the healthiest relationship may have to deal with at one point. A comic focusing on relationships will eventually have to come across some of those problems, or there will be little to no tension in the story (which is why I prefer romances that have multiple plot lines instead of focusing on the character's love life).
All of this is just a really long way of me trying to say: I very rarely see comics where I truly feel the characters are being unhealthy for each other, unless that's the whole point of this story (maybe the abuser is even the villain). Because of that, I don't have that big of a problem with this trope.
I draw a line at the comics that are seeing rape and abduction as something that is acceptable or redeemable. I don't get it and can only shake my head at those. Maybe someone can explain them to me, I really tried to understand and I had to give up.