Off the top of my head, I don't know of scientific studies that have tested this. But even if there were, I don't think they'd necessarily be meaningful in comparing a particular store-bought culture to a particular "heirloom" culture.
The general thing to remember about store-bought cultures is that they are bred for rapid and consistent fermentation (generally in very clean and precise conditions), and they are propagated on a regular basis. (That is, they generally aren't expected to survive intact for many days or weeks in a fridge before growing again.) They also tend to have a few very specific bacterial strains added in specific amounts, and that mixture is kept constant. (Usually, companies add bacterial cultures directly for each new batch, rather than inoculating with a "starter" from an old one; this ensures consistency.)
"Heirloom" cultures may have a greater variety of microorganisms, some of which may be adapted to surviving longer times between batches or fermenting in less precise conditions.
I'd say that when store-bought cultures "fail" or become "less potent" after a few batches at home, it could be due to a few different factors:
- Culture was stored too long between batches, and some components died off
- Storage conditions between batches were problematic (e.g., less optimal temperature, bad pH)
- Less precise culturing conditions caused the "equilibrium" between various microorganisms in the culture to be messed up, perhaps leading to overgrowth or undergrowth of some elements, making the resulting product less consistent
- Other microorganisms were introduced (usually inadvertently through contamination), which compete with or otherwise imbalance the growth of the original culturing ones; sometimes storage can also affect relatively relative populations here too
There's no guarantee that a product advertised as an "heirloom" culture will necessarily do better for your particular yogurt-making regimen. I have certainly heard of people having mixed results ordering online yogurt cultures. But if it is a culture that has gone through many cycles of less-precise ("home") propagation, it may last longer and be more adaptable to various changes in yogurt-making regimen than the specific mixtures found in commercial store-bought yogurt. Such "heirloom" cultures have been literally "bred" for a different purpose.