I'll have to disagree with Doughead here. This actually sounds normal to me, and I don't think you need to be concerned, just carry on using your watch as usual for now.
The fact that you got it new from a shop doesn't necessarily mean it will or should be at full charge, this would only be true if you got it directly from the production factory (which isn't likely!). Shops will be putting solar Gs in storage hence the charge will be gradually in decline even in power save mode.
anyway, since you can see it go up to the top bar, it means it should be charging normally. and even if the bars are full, it isn't an indication that it is fully charged, rather, you should interpret this as an indication of the charge just being 'high', something like >75%. If you consult the manual, it will state the the rechargeable CTL1616 battery (Doug, take note

it is a battery, just like regular non solar Gs!) will take different amounts of time to charge depending on the lightsource it is exposed to, anything from a few hours to several days, even weeks. The strongest source would be outdoor sun on a clear day, and even then it would take a few hours to charge to full.
There are a few things you can do to help it charge faster as well, such as turn of your alarms and hourly signal, turn off auto EL, avoid excessive use of EL etc. I find that many of my solar Gs will run down to 'medium' even if I don't use them much, but this is hardly surprising because of the climate where I live, especially in winter (I'm in the UK! ^^), but once the summer comes, they'll all charge back up!