In this particular case, I’d say there is a difference in meaning, though only a nuance. It appears with deontic modal verbs.
How often should I feed her?
– is a simple, straightforward question that asks for the answer to something you do not know.
How often should I be feeding her?
– implies that the asker thought they knew the answer, but clearly what they thought was right can’t be correct (as evidenced by the cat continuing to gain weight), so they are now asking what the actual correct answer is.
This is much like the distinction in the following, very similar, constructions:
You’re such a bad dancer, Billy-Bob! You constantly put your left foot first when you ought to put your right foot first.
This phrasing makes the two verbs parallel: every time you’re supposed to do X, you do Y instead.
You’re such a bad dancer, Billy-Bob! You constantly put your left foot first, when you ought to be putting your right foot first.
This phrasing disjoins the two clauses. The meaning is that you do Y (in general), but what you really should be doing is X.
While I’m sure these different uses of the progressive with deontic modals has been named by someone at some point (what hasn’t?), I don’t know what it is called.
(Obviously, other modals, even deontic ones, may entail other differences in nuance between simple vs. progressive constructions. The difference between “He must grow old” and “He must be growing old”, for example, is a completely different one.)