Some tools will grey-out certain options. Prime example is if you are
in the Text tool (ready to type text) and you try to save without
going back to an 'open' tool such as Marquee...

You might want to check what tool(s) are active when you try and save.

Another option: Try saving the image in a flattened format first, then
save-and-close the master .psd file. Open saved image and see if you
can do your 'Save for Web' from that. Nasty, ugly, but usually works
when all else fails.