Why do Tom and Daisy stay together?

We're never told exactly why Daisy and Tom stay together. We know from early on in the novel that Tom is having an affair with another woman. We know that Daisy knows about the affair, though not who the woman is, and we learn that it makes Daisy unhappy. Later, we find out that from the earliest days of their marriage, Tom found lower-class women to have affairs with. Nevertheless, he seems to consider Daisy a highly cherished possession.
Beyond that, they seem to have a special bond. We see this on three occasions. The first is when they come together to one of Gatsby's parties for the first time. Neither of them like the party—they seem to think it is beneath them, full of vulgar people. Because Gatsby suddenly sees his parties through Daisy's eyes, he abruptly stops having them.
The second is after Tom has discovered her affair. He knows how to get Daisy back. At the Plaza, he says:

And what's more, I love Daisy too. Once in a while I go off on a spree and make a fool of myself, but I always come back, and in my heart I love her all the time.

When Gatsby presses Daisy to say she never loved Tom, Daisy says:

I did love him once but I loved you too.

She goes on:

"I can't say I never loved Tom," she admitted in a pitiful voice.

Tom then moves in for the kill and verbally attacks Gatsby as a criminal. Gatsby tries to defend himself to no avail. Nick states that,

with every word she [Daisy] was drawing further and further into herself, so he [Gatsby] gave that up, and only the dead dream fought on as the afternoon slipped away, trying to touch what was no longer tangible, struggling unhappily, undespairingly, toward that lost voice across the room.

At this point, Tom knows he has won and feels safe enough to let Daisy and Gatsby drive home alone together.
The third point that shows their bond is when Nick, after the accident, sees them through the pantry window:

Daisy and Tom were sitting opposite each other at the kitchen table, with a plate of cold fried chicken between them, and two bottles of ale. He was talking intently across the table at her, and in his earnestness his hand had fallen upon and covered her own. Once in a while she looked up at him and nodded in agreement.
They weren't happy, and neither of them had touched the chicken or the ale and yet they weren't unhappy either. There was an unmistakable air of natural intimacy about the picture, and anybody would have said that they were conspiring together.

From these episodes, it seems clear that a bond of class, of familiarity, of intimacy, and even of love holds Tom and Daisy together. Daisy is weak and Tom protects her.