Critical Dilution is the phrase that we use on the Wiki to refer to the dilution below which adding more detergent has rapidly decreasing influence on the soap film thickness.
Currently, critical dilution is a fairly rough but useful measure. For Dawn Pro and its equivalents, the critical dilution seems to be somewhere around 16:1. It is influenced by pH for many detergents as the effectiveness of many surfactants is heavily influenced by pH.
Critical Micelle Concentration and Critical Dilution (Jan. 2015). It was previously our understanding from a discussion on SBF, the Soap Bubble Fanciers Yahoo Group (RIP) that the relationship between film thickness and dilution was related to surface tension. This seems not to be correct. However, the relationship between dilution and film thickness does seem to be correct and has held up to repeated scrutiny. New discussion on SBF has raised doubt as to whether the variations in film thickness that result from changes in dilution are related to surface tension. It has been suggested that the changes are not directly related even though the contours of the function curves may be similar (dilution vs. surface tension and dilution vs. film thickness). Apparently, even our most dilute concoctions (even 50:1) are still under the Critical Micelle concentration -- and tests have shown that there is no practical difference in surface tension with the different dilutions used by bubblers.