From Quora: My Answer to "Is it better to ask a letter of recommendation early or when you begin applying for things like jobs or schools?"

It’s always better to ask early. First, find out if the teacher/professor would be comfortable writing you such a recommendation. Hopefully, if they don’t think too highly of you, they’ll at least be kind enough to suggest you have someone else write it for you. You should ask the person you want to write a letter when they’d have time to do it (some teachers and professors have a certain time of year they reserve for such things, and aren’t happy to write letters outside that time period). Of course, let them know when you need the letters written.
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Anyway, it’s always better to ask earlier, rather than later, because there’s no guarantee they’ll have time to do it if you spring the request on them at the last minute. No one’s going to skip a vacation, dinner with a spouse/significant other, time at a second job, etc. just because you didn’t plan ahead far enough. In case you haven’t seen this already, you should know that practically every college office where the staff deals with students (think the registrar’s office or the bursar’s office - the offices that deal with class registration and tuition money/financial aid) has a sign posted that reads “Failure to plan on your part does not create an automatic emergency on my part.” Treat your teachers/professors/supervisors/whomever you intend to ask for a recommendation the same way - don’t assume they’ll drop everything to help you. Start early. Hope this helps!