Correct me if I'm wrong, but in this context, wouldn't "as chaves" be understood as "[her] keys"? We wouldn't idiomatically translate "the woman forgets her keys" as "a mulher esquece as chaves dela", right?
Also, "the woman forgets the keys" sounds quite odd in English if they are indeed her keys.
But they need not be. Maybe they are the keys to the office, to some storeroom, ...
"forgets always" is not a construction you would normally use in English. The word "always" almost always comes before the verb. You can put it at the end of a sentence to emphasize it (for example, "I want to be in your thoughts always"), but normally it would come before the verb: "I always want to be in your thoughts." I suppose you could say, "I want always to be in your thoughts," but to a native English speaker like me, it sounds awkward.