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No it's not normal. You should really hook it up to a tender but, before you go and buy a new battery you should take the old one out, charge it fully and leave it for a few weeks if you can.
Measure after a time and see if it did loose charge. I would hate to see you buying a new one whilst the problem was a sneeky drain caused by the bike's electrical system.
Or have the battery tested properly.
7 Surprising Harley-Davidson Products that Are Not Motorcycles
Slideshow: The bar-and-shield logo shows up on far more than motorcycles, some of the company's most unexpected products have nothing to do with riding.
Slideshow: From the troubled AMF years to modern misfires, these bikes earned reputations for reliability issues, questionable engineering, or disappointing performance.
Crazy Bunderbike Build Looks Amazing, But Is It Impossible to Ride?
Slideshow: The Swiss custom shop has taken a Harley Softail and stretched it into something so long and low that it looks closer to a rolling sculpture than a conventional motorcycle.
Engraved Rebellion: Inside Bundnerbike's Glam Rock II
Slideshow: A standard cruiser becomes an intricate metal canvas in the hands of a Swiss custom house known for pushing Harley-Davidson platforms far beyond their factory brief.
Slideshow: Harley-Davidson's challenges aren't abstract; they show up in dropping shipments, shrinking dealer traffic, and strategic decisions that aren't yet translating into growth.