There are definitely cases where it doesn't make sense to translate その into an English demonstrative adjective.
アインシュタインとその人生 Einstein and his life ('his', I guess, is a possesive pronoun)
まあ、その、なんていうか... Well, oh, you know... (filler word)
Another thing to point out: Japanese speakers tend to use personal pronouns (including possesive pronouns) less than English speakers. Sometimes Japanese speakers might use その in cases where 'your' might be more natural in English.
そのケータイ、いいねぇ Your cell phone is cool!
If you're really asking whether, when translating to English, その should often be translated to the article 'the' instead of 'that', then I would say usually no. If there's a need to specify which object is referred in Japanese, there's a good chance the need is there in English as well. But then, it really depends on the situation and context, so it's hard to give exact rules.
is gramatically fine per se, just as the job/that job/your job all work in the English version. But その仕事 sounds more like 'the task you're working on right now', where just 仕事 could be taken as 'your job' (i.e. your position). Again, hard to say exactly without more context.