When is an event so old that the phrase "the other day" no longer applies?

I went to the dentist half a year ago, but when I mentioned that to my girlfriend, I said that I went there "the other day." She said that events which happened such a long time ago definitely did not happen "the other day", but this violated my understanding of the phrase; I would use it to refer to any event that happened in the relatively recent past—maybe at some point in the last two years. My girlfriend would not use it to refer to any event that happened less recently than last month. Neither of us is a native speaker of English, so I would like to ask: which understanding is closer to common English usage? When is an event so old that the phrase "the other day" no longer applies?

Note: I understand that phrases like this are of course not clearly defined and usage may depend on the speaker and the context. But nevertheless there must be some kind of vague time frame at work here; one would not say that an event which happened twenty years ago happened the other day, but it would be fine to say so if it happened a week ago. So what I want to know is if there exists a bit tighter limit on this time frame.