Personally, I don't think that time has any ill-effects on oil, unless it just sits long enough in between drives and collects moisture. I would go by how many miles you think it should be changed by. You can go by how the oil looks on the dipstick to tell if it needs changed, or in other words, how dark it is on the dipstick. Many people think it is only because the oil breaks down, but it also cleans the inside of the engine. So I wouldn't go by an extended period of time. Just because it is synthetic oil, doesn't mean it will be good for 10,000 miles because that is 10,000 miles of dirt in the oil. When I use synthetic, which I use in my WRX, I don't go over 5,000 miles and try to change it between 4 and 5,000. I may be changing it quicker than other people, but it doesn't hurt the motor any to have clean oil, whereas it can hurt it to have dirty oil. Just my opinion.
BTW, the 3 month/3000 mile is just an average. National average is that a car owner will put 1000 miles on their car a month. Thats where they get 3 months. Like I said above, I think the mileage is more important than the time period. Just change it whenever you feel the oil is getting too dirty.