Battery questions.

[caratz]

My GT doesn't get ridden much nowadays. I purchased an original BMW CanBus charger when I got the bike, but never used it until last week. When I put it on the first time, it had NO charge whatsoever. After 24 hours I had full charge on the battery.

Yesterday, I used the bike for shopping. That means lots of short distances and stop and starts, with really not much opportunity to run the bike up.

Plugged in the charger upon returning. Again it showed less then 1/3. Two questions : is that normal considering it was fully charged last week ?
Can I leave the CanBus charger plugged in permanently without damaging the battery ? I seem to recall that the BMW charger has a battery tender ?

It is strange however that the bike was starting without problems, even though the charger was showing less then 1/3. That was also the case before I recharged it last week.