Dear Carl, the correct paper to derive the 0.1-second lifetime of the anti-Hydrogen atom in the gravitational field is described after the very sentence you quoted.
There is a "" symbol which means that the sentence is justified in the reference number 20 in the list of literature at the end of the paper you quoted. So the correct paper that answers your question is
Quantum reflection of ultracold antihydrogen from a solid surface
A Yu Voronin and P Froelich 2005 J. Phys. B: At. Mol. Opt. Phys. 38 L301, doi: 10.1088/0953-4075/38/18/L02
which is fully available online - click the last link for the PDF file. At distances longer than 15 nanometers from the metal, the Casimir-Polder potential has the form $-74/z^4$ in atomic units. At shorter distances between 1 Bohr radius or so to 15 nanometers, the potential becomes $-0.25/z^3$ in atomic units - a van der Waals form.
Only at distances shorter than 1 Bohr radius or so, the anti-Hydrogen behaves differently than the Hydrogen, and is annihilated. This portion of the potential is not probed in the 0.1-second case: note that to get annihilation, the positron must approach the electron at a shorter distance than the Bohr radius - comparable to the Compton wavelength of the electron (and even shorter, nuclear distances if we want to annihilate the hadrons). The authors calculate the reflection probability as a function of the kinetic energy of the anti-atom. The lower energy/temperature they have, the more likely they will bounce off. For low enough kinetic energy, the reflection probability is as high as 0.99987 (a table).
In those cases, one doesn't probe the short-distance portion of the potential. So the answer to your question why there's no annihilation is the same as the answer to the question why you don't get fusion if you fill a tank with the Hydrogen gas.