Mine does stay fresh, but I don't use a lot of product (or a heat protectant) when flat ironing...a little argan oil and shine serum after I'm done. I know that's probably blasphemy here, but it works for me.
I don't flat iron more than 4-6 times a year. To maintain, I make Bantu knots at night, sealed with a little argan oil. The more product I use, the stinkier and stringier my hair becomes.
But if it does start to smell from just being out and picking up scents, I use a little dry shampoo to keep it fresh. Or go all out, slap some really good smelling butter on it, and do two French braids and wear a braid out until my next wash.