The question of constant targeting– That is, when an effect existing on a creature, an object, or an area is always confirmed or denied, if the destination is valid, and if this is denied, something (scatter, suppress, explode, etc.) will happen to the target Effect As far as I know, it is not generally mentioned anywhere. (Specific effects can Mention constant targeting, but for example, the skill of a known share spell can not affect the 3rd level Sor / Wiz spell prototype [trans] (spell Compendium 161).)
The D & D Main FAQ– which some people deal with – addresses this idea, albeit at an angle:
If, while under the effect of a spell that depends on the type (such Person hold), my character is being transformed by another creature type polymorph, does the effect of the spell persist?
Yes. A spell only checks if you are a valid target when cast. If you later become an illegal destination (for example, over the polymorph Magic) the spell remains in effect. (87)
(I'm not aware of the origin of this question.) If nothing in the rules says constant goals is one thing and that judgment, that – for this particular case anyway – it is not One thing, this DM feels good about governing If the target of an effect was legal at the time the effect was activated, the effect will persist even if the target becomes illegal later,
In short, this DM – as well as yours – would also cause the familiar to continue to benefit from the common spell, even if the familiar no longer had the skill spell after receiving the common spell.