Think back, far back, to TEotW. Remember Ishy in the heads of our three young heros, in their OWN dreams, NOT T'A'R? (correct me if I'm wrong, oh quotemasters, but you can't bring someone into T'A'R against their will, can you?) In any case, his harrassment of their dreams stops shortly before they reach the Eye, presumably because of Moiraine's protection (which, if you recall, hasn't worked too well in the past). Now, on to my theory:

The Dreams stopped because the Forsaken were being freed at the point. Lanfear later takes over planting dreams in their heads, but we know of her as a skilled Dreamwalker. Ishy, we never hear any mention of skill in that area, but he obviously did a horribly difficult task: controlled another person's dream. Egwene frequently and embarassingly capitulates to the whims of the dreamer who's mind she enters (e.g. Rhuarc, Gawyn), and they aren't conciously TRYING to make her do anything. Rand (and, presumably, the others) are semi-lucid and trying actively to make them stop, but Ishy keeps coming.

We don't know WHERE exactly Ishy remains for the 3000 years he's half-bound.

My conclusion is this: he was in T'A'R, similar to the Heros of the Horn who stay there, but less firmly held and without the prohibition on being seen (hence why he could enter dreams, and talk). Existing almost wholly in T'A'R, he might either

A) gain natural strength in Dreamwalking from being a creature of dreams

OR

B)have 3000 years to practice.

I think it likely it is either B or a combination. However, this leaves us with the problem of why he hasn't entered dreams since then. Perhaps he is not used to doing it from a living body, has not had a reason to, or can't enter T'A'R easily anymore.