The Rules Are... Ambiguous
The Universal Monster Rules regarding poison say that
... The saving throw to resist a poison is usually a Fort save (DC 10 + 1/2 poisoning creature's racial HD + creature's Con modifier; the exact DC is given in the creature's descriptive text).
The only ambiguous part of that rule regarding the centipede as a normal creature is the 'usually a Fort save' segment; the rest specifies how a poison's save DC is calculated, and that it will be calculated in the creature's descriptive text. Recalculating on a change of racial HD or of Con is the correct reading of the rule.
The rules are silent, however, as to whether the effective HD for effects are racial or not. One argument in favor is that the familiar has only one type of HD, and so they would be 'effective racial HD.' The argument against it is that the rules don't say that they are.
Both rulings have merit; the permissive ruling helps the familiar remain relevant as the master's level increases, and the restrictive ruling helps keep 'the rules don't say I can't' from being a useful argument.
The clauses from the familiars section regarding HD is dichotomous:
... It retains the appearance, Hit Dice...
Hit Dice: For the purpose of effects related to number of Hit Dice, use the master's character level or the familiar's normal HD total, whichever is higher.
The second clause would override the first, depending on the definition of 'effects'. Since there is none in the glossary, extrapolation is necessary.
Within the glossary alone, there are hundreds of instances of the word 'effect' or 'effects'. Looking at the Afflictions Section, afflictions, including poisons, appear to have effects.
Thus the effects of poison that are related to HD should be calculated from the master's HD, when higher.
It's still ambiguous though. If they'd just define what an 'effect' is, then these questions would be a cakewalk.