Does this make any sense?
I have been keeping ignoring you.
Besides that it sounds awkward, my Chinese buddy who knows more grammar rules than I care to list said that the phrase is grammatically correct. Can anyone tell me why?
This doesn't seem to be correct grammar. The sentence in a normal present perfect continuos structure should be written something like:
Grammatically in a context like this, you cannot combine two progressive verbs, in this case keep and ignore, side by side as in this construction.
It's not really good English grammar. It does feel awkward, as has been noted. That's the giveaway, to a native speaker.
And of course nothing like this is treated in school grammars, because they're still talking about English as if it were Latin, with six tenses, two voices, three or four cases, and all sorts of other zombie phenomena. This educational deficiency afflicts both native speakers in Anglophone education, and foreign learners in ESL classes worldwide.
The reason it's ungrammatical is that it runs afoul of what Haj Ross called the Doubl-ing Constraint in his paper on the subject. (Unfortunately, ERIC doesn't have the full text of the paper available, for some bureaucratic reasons, but the link shows the abstract.)
The gist of this constraint is that under certain circumstances (which the paper spells out in detail), one can't use two present participles (-ing forms of a verb) together, with one governing the other.
I.e, the following are just out:
Even though comparable sentences without double -ing are fine:
There is a lot of speculation about how and why this rule operates, but mostly it seems it just interferes with the parsing routines of many native speakers; i.e, it's a purely syntactic rule, totally unconscious and automatic, concerned solely with form, not meaning.