Last year (probably around August) I tried rooting some cuttings from a keraji. Unfortunately, it being August in S. Georgia, conditions were typically hot and dry and most of the cuttings quickly dried out. The lone remaining cutting, about five inches tall and 1/4 inch in diameter, has just stuck around. It lost its leaves shortly after being planted, but has stayed green throughout. This past spring, it sent out a 1/4 inch of new growth from one bud, but that, I suspect, was eaten by a snail, as it simply vanished about three days after it appeared. Since then, it has remained as it ever has been - green, with taut skin, no rot, no growth, no leaves.
I tried a small dose of fertilizer over the summer hoping to spur new growth, but to no avail. Any suggestions?

Hot and dry are bad conditions for growth . Hot and humid (tropical) are conditions conducive for good growth. - Millet

What setup were you using to root your cuttings?

They should never be allowed to dry out. They need a very humid environment.

Did you just stick them in the ground outdoors? In Pots? Did you put a baggie on them?

Need more details.

They were just stuck in pots and placed in the coolest, dampest part of the yard, but it was still hot and dry. Conditions clearly weren't optimal, and I just didn't bother taking additional steps to control humidity, such as bagging the pots. But my question is more regarding the dormancy that this cutting seems to be in. The cutting is obviously still alive - again, taut, green bark, no rot, put out some growth this spring, ~ six months after being planted - but nothing since then.
This summer, I've tried various conditions - starting it out in a cooler, damper spot, then moving it to full sun to try to "wake it up", I also tried a very small dose of fertilizer.
Any other suggestions? Giberellic acid, perhaps? Waiting for another winter/spring cycle?

Gibberellic acid won't help. What gibberellic does is elongate the inter node. - Millet

Via an increase in cell division, yes, which might simply deplete what - presumably few - carbohydrates this thing has left and provide it with merciful death, but just might give it the kick in the pants it needs to get growing.
Basically, I was thinking that since the natural abundance of giberellic acid tends to correlate with the break from dormancy ("dormancy" in the case of citrus) in spring, that an induced increase might fool the cutting into "thinking" it is spring and time to get growing. Perhaps surprisingly, research seems to support the idea; see the note at the end of the section on winter dormancy: http://www.crec.ifas.ufl.edu/academics/classes/hos6545/pdf/cooper.pdf. (N.B. that I haven't been able to find a copy of the article cited.)

This is Bill Adams' method.
1. Late spring or end of summer for outdoors, warm but not too hot.
2. Select actively growing wood for cuttings.
3. Select two or three nodes plus about 2 to 4 inches in soil.
4. Trim most leaves but save 1 small or 1/2 large leaf for food.
5. Use liquid Rotone, then stick in soil in bright indirect or filtered light.
6. Cut the bottom off a 2 liter plastic drink bottle and place firmly over cutting.

It has been many years, but if the hormone says to use straight, do so. If
it says to dilute, use about 5 or 10 to one.

Bill Adams methods works great. I place a small bamboo or plastic stick in the center of the pot with about 6 or 7 inches above the top of the cutting an place a produce clear bag complete over complete pot tucking the bottom of the bag under the pot. Works fine.

I've used the 2 liter bottle method with great success. I've rooted a Manila mango, Eureka lemon, Chandler pumello and , just sprouted a few weeks ago, Fuyu persimmon. And I've rooted numerous figs using much smaller water bottles.