Question on the mechanics of an attack.

Since I started playing, last night was probably the single best play experience I have had.

Unfortunately, I didn't get to log in until late, and there were only a few squad members online.
We were defending Aachen, and at one point, managed to locate a U.S. FRU, and just pick off several soldiers like it was a shooting gallery. Probably the most enemy I have ever seen in the game, and it was a lot of fun.

Anyway, after going back and forth with cat and mouse games taking bases and ball bearing factories, we finally capped everything in the city, and about a minute later, the attack was withdrawn by the allies.

Now, my question is as follows:

What makes an enemy side eventually withdraw instead of pounding a town until they have it?
I am assuming it is attrition, but can someone explain the "big picture" part of why attacks fail and a side will eventually withdraw?

Thanks.

Supply runs out and/or another Juicier potential target comes about

Usually, when either side launches an attack, they try (and usually fail) to gain an element of surprise by rushing in with a lot of infantry and capturing as much as they can before the other side can raise an adequate defense. If they are successfully repulsed, they will usually withdraw the attack and try again elsewhere, especially if they suffered significant casualties in the effort.

Once the defenders have managed to dig in around the perimeter of the town and spread out into the countryside, continuing the attack becomes much more difficult, due to the way the game is designed.