I'm vaguely aware that the usage of furigana is based on the intended target audience. The younger or less likely literate the target audience the more furigana are employed. But is there a system to decide which words receive furigana and which don't? In intermediate novels I find it not unusual to find furigana on words that were printed without just a few pages earlier. Is this done because somebody decided that that word/reading is less likely to be known in that context, or is it pretty "tekitō"?
I can't answer on the particular case of a word that would receive furigana after not receiving it earlier (the opposite, however, is naturally quite common): assuming the words are rigorously identical and identically read both times, this sounds more like an oversight than anything.
As for the general rules of adding furigana, they are pretty straightforward, depending on what kanji level can be expected from the reader.
One should probably separate:
Readings targeting children and young adults (about anybody at High School age or under) have very fluid rules, as far as I can tell. Overall, they will try and follow the regular Japanese school curriculum, which is very specific about which kanji must be mastered by when. But since their target demographic itself might not be all that exact, they will probably err on the side of caution and annotate all non-kyouiku kanji.
Regular readings: newspapers, novels, manga for adults (adult-age, not adult-themed) etc. will generally put furigana only for highly irregular readings and kanji that are outside of the jouyou set. I believe adding furigana to non-jouyou kanji is even a requirement by law for newspapers (but I cannot find a source for this just now). Of course, the socio-professional status of the intended audience will probably play a role in how generous with extraneous furigana they are (e.g. cheap weekly magazines etc.), but I noticed such materials just tend to skip the kanji and go straight to kana when needed...
It must be said that the strictness in kanji requirement (compensated by the use of furigana) has dramatically decreased over the past 30-40 years: to convince yourself, just compare a copy of any 70s-era manga (e.g. Tezuka Osamu's Black Jack) with modern day mangas targeting the same demographic ("shounen" - young adult): the latter have furigana all over (anything beyond Jr High School level, essentially), while the former barely bothers putting furigana on even the most obscure proper noun kanji (let alone anywhere else).
Edit: there's been much debate in the answer below, regarding the existence of clearly-defined official guidelines (as opposed to obscure in-house rules). At least for newspapers, I stand my ground and reiterate: Jouyou kanji is the officially agreed base set of kanji to be used in Japanese publications, with some modifications clearly defined and agreed upon by the association of Japanese newspaper editors (source: Wikipedia Jp). One could argue that there is yet another small decision-making step from "kanji that people aren't expected to know" to "kanji that need to be furiganised", but frankly, I'm not going there.
The thing that makes this a difficult question to answer with authority is that no one can provide evidence of something not existing. I can't prove a negative, so if someone can find any evidence of a system (with universal application, not just someone's in-house policies), then please do so.
Otherwise, until then, I am just about 100% sure that there is absolutely no system at all. It's entirely done, as you suggest in your question, based on the creator's (including all production levels of authors, editors, publishers, etc...) assessment of whether or not the reader can read the kanji.
Further, not only is there no system or agreed standards for when furigana should be employed, there is equally no system for when words that have kanji are written entirely in hiragana.
I am currently reading the adventures of Tintin in Japanese, and they make all sorts of seemingly random (to my non-native language level) choices about which words have furigana, which words are offered in hiragana, which words are never given furigana, and which words are given furigana once but not again. The people who translated it went case by case for each sentence assessing the reader's ability to read what was offered.
And that's pretty much how it's always done. The only "system" you might find would be within some publisher or company and applied to all their own materials, but that would be just as arbitrarily decided as any other publisher's choices.