Battery replacement question

[Agrare]

Ok, so i've had the feeling my battery has been on it's way out. About a year and a half ago it was dead one morning and required a jump. It's been ok since (it's possible I left a light on but don't think so) except I notice, especially in winter\cold weather when not driven for a little while it takes a while to turn over.

I don't really drive that often as I take public transportation to work, but I drive it generally twice a week during the week and probably at least once on weekends.

Anyway, last night I had the lights on, engine off for maybe 15-20 minutes and they started to dim. I required a jump to get it started (mainly because the doors auto lock after so long and did so with the keys in so was probably over an hour when I got in, but I could visibly notice the battery going dead after no more than half an hour).

The car is a 2005 mini cooper convertible (purchased in april) the battery is the original

So my question, with the background above do you think it's just an old battery that needs replacing or should I bring it in to have the alternator checked out?

sorry for the long post, just wanted to give all the info, thanks in advance for any advice.

-Agrare