The first place I'd look is any crevices and any non-ss parts. What do you normally put in this cup? A water cup shouldn't smell (unless you have hard/sulfuric water), but milk or juice can both attract bacteria (and smell horrible) and will need to be cleaned more thoroughly.
But, I did notice that over time, my DH's SS coffee cup built up a deposit. I was having a really difficult time getting it off, and even the dishwasher wasn't touching it. So I wound up putting about a Tbs of BS into the cup, filling with HOT water and letting it sit overnight. Then just a light scrubbing with a bottle brush and the water turned BLACK. I wound up having to do it twice because the deposit was so bad, but after 2 soaks/scrubs/rinses, the cup was actually shiny again.
I also have a cream whipper that is metal - that for some reason after a few uses started smelling like rotten milk. Didn't matter how much soap/hot water/scrubbing I used on it, the milk was clinging to it. For that item, I wound up having to run it through the dishwasher as the only thing to get it clean - even though it's technically not dishwasher safe.
My point being that if one thing doesn't work, try something else.