conform points out that anaerobic mediums, such as this flavoured oil are the perfect breeding ground for the botulism bacterium. The bacterium would need to be present on the garlic in the first place, and would then have to multiply over time, until it reached harmful - possibly fatal levels. The choice is up to you. Botulism is statistically a very rare food-borne disease, but if you want to be super-cautious, use this oil within a day or two, keeping refrigerated as above. I'm still keeping mine as I always have - for up to a fortnight.
unperson has expanded at length on this point, and I urge you to read the very thoroughly researched Flavored oil and botulism to get the full idea. However, permit me if I may...
There is a risk, yes, of creating a little botulism factory when you make garlic oil. But there are risks, and there are risks. unperson himself stated that "...Botulism is very rare (about 20-30 adults in the US get it from food each year) but is fatal in about 5% of cases...". That makes for a generous 1 to 2 fatalitiles per year, in a country of what? How many souls do you guys got now? 290 million or so? Look at it another way - 21 people perished in avalanches in the US in the year 2003/2004 ¹. Let's get realistic here.
I have made this stuff once a week, every week, in 2 litres batches, for the last 10 years. I have often kept and used it for up to 2 weeks. No one yet is sick or dead, from oil or avalanches or otherwise. However, I do play it safe.
I always keep it refrigerated when not in use. I always throw it away when it looks less than perfect (bubbling, discoloured, or otherwise unsightly). If you too follow these simple guidlelines, I have a very good feeling about you lasting to eat another meal.