The very first time i was ever hit in anger was when i was about 20 years old. It was a guy i was dating at the time and it just came out of the blue. There was no set up, no way to see it was coming. Even at this great distance from that time i look back on the balance of that relationship and realize that his version of abuse was summed up in that one beating i took at his hands. That was also the last time i saw him. I left that house that day and never went back, never saw him again, nothing. Taking your frog analogy into consideration, that was me being thrown into a pot of boiling water. I jumped out.

Fast forward to 15 years later. There was no abuse during that 15 years, although several relationships came and went. My ex was so sweet, kind, concerned with me, for me, because of me. When the abuse started it was slow and methodical. The "frog" version of me was being slowly boiled. When you get used to it in little bits, it's just life. It's just the way it is. The more i compromised the more he pushed the limit. Not in one big shove, just one little finger and so gently that i didn't recognize it. It is all done in the name of compromise and of course we all know that compromise is good for a relationship, right? So maybe this isn't unusual, this isn't bad, this is just how a relationship should be. That moment, right there, started my decent into the hell that was later to become my marriage. By the time he actually raised a hand to me, i was already boiled to mush in the pot and accepted it as my due. When he would call me horrible names, it must be true. When he would take my cell phone, laptop and car keys away and lock me in the house while he went and got drunk - it was for my own protection. I believed he was doing it because he cared so much. I know how psychotic this all sounds at this great distance, but it is absolutely what was going on in my head at the time.

See how different those 2 incidents are? The first one came out of the blue. The second i was set up for in a methodical way. Even when i started to see what was going on in my marriage he always had a way to explain it. At the end of my marriage, after i had left he quit drinking. Problem with that was that he didn't really think he had a problem. He told me he did it for me. His quitting drinking was just another form of control, he thought it would bring me back.

So to answer the original question, we stay because we see potential in the relationship. The intensity of it, the obsessive nature of it, is so sweet and so overwhelming that we willingly suspend any semblance of boundries that we have for other relationships. I would never in a million years allow a friend to get away with what he got away with. My complete and absolute lack of self-esteem was replaced by his vision of me. He wanted a perfect wife and believe me, i was the perfect alcoholic's wife. He said jump and would drag out the trampoline. I could handle anything he threw at me and turn on a dime in any conversation. Took me a very long time to figure out that this isn't healthy. That was me trying to be a blank screen where he projected whatever he wanted and i would just turn into that. That was no "me" in that equation.

Speaking only for me, i was re-playing my abusive childhood. Low self esteem lead me to partners I thought I could save from themselves. I had taken on this responsibility when young, towards the adults in my life.
Within 6 months of dating a psycho, I found myself driving across the country to escape his grip on me. That was my wake up call.