The feat Improved Familiar (DMG 200) says that
Improved familiars otherwise use the rules on page 52 of the Player’s Handbook, with two exceptions: If the creature’s type is something other than animal, its type does not change; and improved familiars do not gain the ability to speak with other creatures of their kind (although many of them already have the ability to communicate).
However, the rules on Player's Handbook page 52 (also here)—the rules that describe what a familiar gains as its master advances in sorcerer and wizards levels—on Intelligence simply says
The familiar’s Intelligence score. Familiars are as smart as people, though not necessarily as smart as smart people.
...The chart and its key making no mention of what happens if a familiar already has an Intelligence score higher than the chart lists.
So can an improved familiar suffer a reduced Intelligence score because of its new position as an improved familiar? For example, does a level 7 arcanist that gains as an improved familiar an Int 10 imp, pseudodragon, or quasit see his improved familiar's Int reduced from 10 to 9?
Likewise, can becoming an improved familiar of a sufficiently high-level arcanist reduce a creature's extant spell resistance? (Honestly, I don't think this is even a concern except in the case of a house ruled improved familiar, but it's the other example that's nonetheless vaguely possible.)
In short, does an improved familiar retain a feature even if a feature would normally be replaced by becoming a familiar?
I'd prefer a rules-as-written answer. It's possible a Sage Advice column or other source answers this question specifically, and I just haven't happened upon it (I can't believe this went unaddressed throughout the game's run). However, if such an official source is unavailable or untrustworthy, interpretations of existing texts and examinations of published creatures with improved familiars are acceptable.