I am writing a novel that includes occasional words or phrases in another language. If I use a footnote to provide a loose translation of the word and that same word appears once or twice more on the same page, do I have to reference the footnote for each occurrence?
Welcome. You do not need to use footnotes in a novel. In fact, they're usually distracting. Sometimes you can do it, but it's pretty unusual. An example of one that worked was really a chapter endnote and it is for a book in the Little House series. It let the reader know that “fever 'n' ague” (which was the topic of the chapter) is now known as malaria.
It's tempting to translate things from other languages but often the best route is to just leave it be. A lot of readers will know it or be able to figure it out, others will look it up. As long as it's not important to the story, you probably don't have to translate it at all.
An example of an author writing in English who doesn't translate is Luis Alberto Urrea. His novels are filled with words and phrases in Spanish. To be honest, I think I got more out of his work because I know Spanish (though I don't know most slang), but it wasn't necessary to know the translations to get the gist.
If you feel it's important to translate, and it's not possible (or too awkward) for a character to translate, you can put the translation in parenthesis after the phrase. If it comes from the character's thoughts, this can work well. If it's from dialogue, it's a bit harder. Don't translate anything more than once.
If you feel you have to use a footnote, do it once per phrase. Only translate words if it's important and there is no cognate to the language you're writing in.
If your novel is peppered with footnotes, it will feel more like an academic book than a story.
First off, I basically agree with Cyn's statement that lots of footnotes can make a text feel more like an academic work than a novel.
That said, you say that the purpose of these footnotes is to help a translator.
Ask yourself: Why would such notes, in whichever form, intended for an extremely narrow audience, need to go into the text the reader sees?
One alternative approach I've seen done with good results is to provide a separate "translator's guide" to your story. There, you discuss things like the rationale for various word choices; why a translator might want to leave certain passages untranslated; the meaning behind specific, non-obvious terms; whether in different cases an idiom should be translated literally or replaced with a similar one; and so on.
Such a guide can be written in a much dryer manner than the prose itself, without detracting from the story you're telling; not least because most readers don't even need to realize it exists. It also allows a translator to take your intent into account, by knowing what your intent is, rather than simply translating the words on the page into what they think your intent was.
You do need to be careful to not make it too restrictive, but if you limit it to discussion of various forms of intent then I don't think that would be a significant risk.