Hemoglobin A2 is a normal variant of hemoglobin A that consists of two alpha and two delta chains and is found in small quantity in normal human blood. The delta gene is found on the same chromosome as the beta gene and just as beta hemoglobin does, delta hemoglobin joins with the alpha chains and forms a useful oxygen carrying hemoglobin. However, HbA2 is found in only small quantities and even though it increases in thal, it is still nowhere near sufficient to supply the oxygen needs of the body.
My guess as to why it isn't be induced is that this gene is already turned on, unlike the fetal hemoglobin (gamma) gene. Induction of HbF relies on turning the HbF gene on. This leads to higher amounts of useful hemoglobin in the body. Since the delta gene is already turned on, it is already producing whatever small amount of hemoglobin it can. I don't know if there is anyway to make the gene produce more delta chains, but its small normal contribution to the hemoglobin level may be too small to make much difference even if there was a way to make it more active.
One interesting note about the delta gene. If there is a deletion of this gene in a thal trait carrier, it can mask the trait in tests as the normal increase of HbA2 will be negated by the decrease caused by the mutated gene, leading to normal HbA2 readings even though thal trait is present.