Now this is juicy (bad pun intended)!
Thanks nud1e, but I've collected some data which may help us understand the problem better and make a more precise diagnosis!
Okay, so this morning, I went to Maplin, fetched the most precise digital multimeter that I could get for a tenner, calibrated it on 20V, and as soon as I got out of Maplin I did some readings on the battery. Remember, I fully charged the battery yesterday afternoon (with Optimate, it took 3 hours), then I had a 1 hour trip to and from town (mostly at 4000rpm) in the evening and then it sat still for the night.
This morning, the trip to Maplin took 20mn, which I did again mostly above 4000rpm (this means 1st and 2nd only, not that I was trying to kill as many pedestrians as possible!). As we'll see, it was irrelevant, but I didn't know this at the time...
So out of Maplin, the battery (engine off) read 12.75V (steady).
I switch the beast on, it reads around 13.80V at idle (within a .20V range).
Note: I start with the choke, and the battery indicator disappears immediately, idle rpm around 1100rpm).
Now comes the juicy bit: I go to 4000rpm, still 13.80.
4500, 5000 rpm (glad my engine was warm), still the same: 13.85, anything between 13.78 and 13.90, but not above).
Now if I understand well, that means that
MY ALTERNATOR DOESN'T KICK IN TO DELIVER THE FULL OUTPUT ABOVE 4000rpm!!!!!
So it may explain better why my battery goes flat: when I THINK I'm fully charging it on the road, making sure I'm above 4000rpm, I'm actually depleting it with all my goodies (GPS, heated grips, ipod) which I try not to use in town. Then when the bike sits for a couple of days, the battery is not full as I think it is, it's almost empty. And that's why it loses its charge so quickly. Does that make sense, or do you think the battery is dead anyway on top of the alternator having a problem?
At least it means that the permanent load (alarm+autocom+nokia) doesn't drain the battery when I'm riding.
Last bit of data:
When I got home after the Maplin trip back, I read the battery again, engine off: it said 13V (so it had charged from 12.75 to 13V in 20mn town riding below 4000RPM).
I'm going to read it tomorrow after 24H and see what it says...
In the meantime, what do you think?