Why had Mr. Burke exiled Prince to the porch?

It's because Mr. Burke couldn't get anything accomplished with the dog continually getting in his way, and he's trying to fix up an old house.

Let's look at that spot in Chapter 7, "The Golden Room." Here's where we find out why P. T. is sometimes on the porch, crying:

"Sometimes he would sneak down to the old Perkins place and find Prince Terrien crying on the porch, where Mr. Burke had exiled him. You couldn't blame the man. No one could get anything done with that animal grabbing his hand or jumping up to lick his face."

So we know that the dog jumps up on people a lot, licks their faces, and grabs their hands. On the one hand, that's very sweet. P. T. is an affectionate dog who loves to be around people and express his love for them. But on the other hand, the dog's behavior is annoying. If you're trying to clean your house, or do your homework, or really, do anything, while a dog keeps demanding your attention-- you're going to get frustrated with it. This is why Mr. Burke puts P. T. out on the porch.

In Mr. Burke's case, in particular, he's trying to fix up the Perkins's house. Jesse describes it as "a broken-down old wreck of a house," so it's understandable that fixing it up will take a lot of work and concentration. Having an excitable dog around while trying to make repairs, keep tools and supplies organized, and so on would be nearly impossible.