Translation:She often has breakfast there.
It depends on where you are. "là" can mean either "here" or "there", and it's mostly context and regional preference that dictates the exact meaning. "ici" always means "here", and whether it's preferred for "here" depends on region and context. I can't imagine my mother telling me to come "là", for example (she's from Gaspé). There's also "là-bas" (sp?), which I've seen Duolingo treat the same as "là", but at least in Quebec, seems to always mean "there" or "over there" (which Duolingo doesn't accept at all).
In English, have is usually a composition verb, used to say I have done something. The construction have + verb indicates a more past tense (le pluparfait in French, if I'm right).
Because all we're using is the present tense right now, it should be "she eats" or "she has" her breakfast. One might also say "she takes" her breakfast (in the sense that one might "take" a pill), but it's a rarely used turn of phrase in English.
My mistake. I read the question for some reason as asking about the validity of "She often takes her breakfasts there," rather than "She often breakfasts there." As for why the latter is not accepted, I can't see a good reason, since there doesn't really exist to my knowledge a pure verb in French for "to (have) breakfast" other than to use «prendre le petit-déjeuner» (or perhaps «manger») like it is here.