It's also not available in Bulb mode (probably obvious
). What mode is your dial on? Green mode is the only thing I've found that removes continuous shooting entirely from the drive mode selection screen (it's just greyed out in Bulb mode) but I don't get any warning about it not being available. It's just not there in green mode, you only have single shot, a couple of self timer modes, and a couple of wireless remote modes.
The manual claims continuous shooting is not available in the "Digital Filter" modes, but it's still select able (it just doesn't work). If you've turned on "HDR", you won't be able to select continuous shooting (it's greyed out). Are you in RAW or JPEG or RAW+ mode? Any of these Filters or other effects turned on?
You can always do a reset of all your settings.