Why do 6-8% of diphtheria patients do not develop natural immunity after being affected?
There are two other, but rather exotic possibilites which explain why people do not develop immunity after an diphtheria infection. These are unlikely to get to 6-8% of the cases which @Masi writes, but I am missing the reference here.

The first possibility are people with chronic renal failure. They have problems with their immune responses since their antigenpresenting cells do not get the necessary co-stimulatory signal by the T-cells. See this paper. People with other problems in their T-cells or the co-stimulatory signal would have this problem, too. See this article.

The other possibility would be the distribution of the antibodies. The diphteria toxin is made out of two subunits, A and B. B is important for making the way of A into the cell, A gets cleaved in this process and fully active. When the antibodies made in the process are mostly against A (and then against parts, which change their conformation after the cleavage), this antibodies are mostly useless to fight the toxin. See this paper.

One (but is complete speculative) possibility is on the toxin itself. It could be possible, that some people are more sensitive to the diphtheria toxin, so that the amounts necessary for the negative effects are too small to trigger an adequate immune response. This is known for the tetanus toxin, where even a survived infection doesn't provide immunity (except when people are vaccinated afterwards) as the toxin is so toxic, that it doesn't trigger the immune system. The caveat is, that the diphteria toxin is about 3 orders of magnitude less toxic than the tetanus toxin.