What a poor, poor sap the red-clad plumber is. Peach has got him wrapped round her pinky finger and he just can't break away. He's a good guy under the spell of a bad woman, and what's happening to him is just tragic. He and Luigi turned up in the Mushroom Kingdom with the best of intentions, and finding it in turmoil, honourably set off to help. But Peach just loved having three men (Well, two men and a giant dino-turtle) pursuing her, and thus a dark, dirty little cycle of emotional abuse was born.
It's not Mario's fault, but he's not helping himself. A self-defeating need to please is at the core of his psychological make-up, possibly stemming from depression or anxiety issues (It's a textbook symptom), and the falsely simpering "Thank You" or half-arsed peck on the cheek he gets from Peach after putting himself through Hell to save her each time is more than enough emotional pay-off for him to convince himself she's still worth it.
In his mind, it means she really does love him after all, and that any day soon they'll be together. She's just busy and has a complicated life is all. Being royal takes up a lot of her time, and he doesn't want to push her when she's getting over the trauma of another kidnapping. And if you don't think she plays up those excuses to keep him hanging on, then you're looking at this from a very naive angle indeed. It's a horrible situation, and a classic example of the abuse cycle. He can probably see what's happening, but he chooses to ignore it because he doesn't want to. As messed up as it is, there's security in the status quo, and as long as the bait keeps dangling, he'll keep taking it.