I have an 09 same problem, the battery (yusha) was only a year old, mine would not start after I gassed-up, the dealer replaced the battery with another one a few weeks ago (yusha) I have a feeling I will still have the problem. I'm glad I stumbled across this web-site, Think I'll be installing a PC680..
I use an Odyssey PC680MJ in my 2007 K1200GT. They work flawlessly and last for many years, far longer than the BMW OEM gel battery or the basic Yuasa batteries. They are definitely worth the cost. I am not sure that an "MJ" battery is necessary - the basic PC680 is good enough. I bought the PC680MJ for the extra "insurance".
Do not ignore remphoto's comments, however. There have been problems with the K1200GT and K1300GT regarding the factory battery wires, and the fix has been to increase the current carrying capacity of the wires from the battery. There are two things that I am not sure of:
* Whether BMW dealers are replacing the wire with a thicker gauge, or double the wire with an extra one. I had read elsewhere that they were adding a second wire in parallel. A quick web search may answer the question.
* Whether BMW will pay for this to be done on older bikes if the problem appears.
For the record, I bought my PC680MJ battery for reliability and longevity. I have ridden all over the country in cold and hot weather (up to 113 F, if I recall correctly) and never had a startup problem. I never had the extra cable installed.
P.S. When you purchase a PC680 (or PC680MJ), you will need to add a small shim - a strip of material between the battery clamp and the battery to get a firm clamping grip on the Odyssey battery. Some people recommend a small strip from an old plastic cutting board. Anything safe and durable will do. I use a strip of plywood, but do not recommend it - one of these days I will change it for something more inert.