This issue comes up often enough that I thought I'd post a quick summary here.Interesting that you used stacking, I thought that was for photomicrography, and this view is about 2 inches across, must have had a shallow DOF!
DOF drops in proportion to 1/(Mtot*Mtot), where Mtot is total magnification = lens magnification * subsequent enlargement.
It's a huge problem at high magnifications, but a significant problem at lower magnifications too.
To take the numbers for Doug's image, suppose you make a print that's 20 cm wide, of a subject 5 cm wide. Then you have Mtot=4.
Using 6 lp/mm as the criterion for "sharp", the maximum DOF is only 70/(4*4) = 4.4 mm, no matter what camera or lens you use.
That 4.4 mm is achieved at an optimum aperture setting that does depend on the camera and lens (more precisely, on the lens magnification & sensor size).
Stopping down less than optimum gives you less DOF because of geometric blurring; stopping down more than optimum gives you less DOF because of diffraction. Stopping down more than about 1 stop from optimum gives you no DOF at all because the whole image becomes so blurred from diffraction that 6 lp/mm is not reached anywhere.
These formulas come from the current best reference on DOF limits, which is Ted Clarke's article "Applying an Abbe Criterion to Photomacrography".
It's enlightening to realize that 6 lp/mm = 12 pixels/mm = 2400 pixels in 20cm. Web resolution is more like 800 pixels in 20 cm, a factor of 3 less. This goes a long way toward explaining why macro shots that are optimized for the web or for video can have large depth of field, relative to traditional prints. Quite simply, they are shot under conditions such that "What you see is all you get!" Any attempt to enlarge the image or to print or display it at higher resolution would just reveal more blur.
You've probably gathered that I'm a fan of stacking. See this article for an introduction to its use in photomacrography.
--Rik