This question's answer varies so widely that you can't truly base your own choice on what we say. Your own child's development and personality are key here -- and our kids may be totally different from yours. If your child turns out to be a climber, a runner, a rambunctious kid, you may have to leave that gate up right until he's ready to start K or beyond! But even a calmer kid only needs to fall down the stairs once for it to be a disaster. If your kid is navigating the stairs calmly and using the rail earlier, take it down earlier. But since he's 10 months -- don't bet on taking it down for a long while to come.
I think a child should be holding onto the railing consistently before you take away the gate. And even then, a child doesn't need to be going up and down steps unsupervised.
Do you also have a gate at the bottom of the stairs so he can't crawl up them and then fall back down them? It's important. We didn't at first, because our daughter wasn't ever downstairs without us when younger, but once during a playgroup at our house, one of the other kids crawled up the stairs and went head over heels back down them -- thank goodness he was OK. We did put a gate up at the bottom after that, just in case!
We left the gate at the top of the stairs in place until our daughter was probably four, nearly five. We also have a door at the top of the stairs and that stays shut even now unless one of us is using the stairs! It's basic safety for adults as well as kids -- no yawning gap into an open space, which is essentially what a stairwell is.
I grew up in a house where there were gates at the top and bottom of the staircase. My mom kept them there until I was probably at least seven or so, I think; I clearly remember them being in place when I was starting school! My mother knew a family whose child of six or seven died after falling down the stairs in their home. It made her very cautious about stairs and kids, and I inherited that caution, I'm sure.