To clarify:  The sulphate end group will protonize only at very low pH, so in that sense SDS charge is not pH sensitive  at "normal" pH. However, SDS micelles are highly charged and the apparent charge of the micelles and the apparent pK of the SDS bound in micelles will depend on ionic strength.

Hydrolysis of SDS results in the formation of dodecanol. The rate of this reaction is, as correctly stated above, pH and temperature dependent. However, at room temperature and neutral to weakly acid pH the hydrolysis rate is quite slow and problems can often  be avoided by using fresh solutions. A sensitive way to check the presence of dodecanol is to measure the surface tension of the solution, which will be lowered by the presence of the alcohol, especially just below the cmc.. The absence of a minimum in surface tension below the cmc is actually a  well-known and sensitive way to verify the purity of SDS samples.

No, SDS is a strong electrolyte and it must not be pH sensitive. This is true, however, only at constant ionic strength and only if the background electrolyte is of much higher concentration than the buffer you use.

So what are your conditions? If you don't keep ionic strength constant, you will get a trend similar to pH sensitive surfactants (but it would be only due to Gouy equation). If you keep IS constant but your counterion-to-H+ ratio changes significantly, you will get a Hofmeister effect (not quite like pH-sensitive surfactant, but yet there will be a pH sensitivity).

If SDS means sodium dodecyl sulphate, it can be hydrolysed at low pH and higher temperatures. The concentration of SDS will then be reduced, and this can appear as the SDS is pH-sensitive.

What type of oil was used?

diesel 

What was the temperature and pH-range?

Sds is always hydrolysing to some degree, i.e. you will have always dodecyl alcohol present at relatively low concentration.

SDS will hydrolyze at any pH. The hydrolysis rate is [H+] and T dependent. Pure SDS is not "pH sensitive", but the interfacial pH will vary with salt concentration. The quastion has to be better defined.

To clarify:  The sulphate end group will protonize only at very low pH, so in that sense SDS charge is not pH sensitive  at "normal" pH. However, SDS micelles are highly charged and the apparent charge of the micelles and the apparent pK of the SDS bound in micelles will depend on ionic strength.

Hydrolysis of SDS results in the formation of dodecanol. The rate of this reaction is, as correctly stated above, pH and temperature dependent. However, at room temperature and neutral to weakly acid pH the hydrolysis rate is quite slow and problems can often  be avoided by using fresh solutions. A sensitive way to check the presence of dodecanol is to measure the surface tension of the solution, which will be lowered by the presence of the alcohol, especially just below the cmc.. The absence of a minimum in surface tension below the cmc is actually a  well-known and sensitive way to verify the purity of SDS samples.