Relaxed hair is even weaker than natural hair that's been dyed hair.
How does relaxer work?
When you have your hair relaxed, the cuticle layer has to be lifted in order to let the relaxer in in. The cuticle layer is then flattened again but the very act of lifting and flattening the layer weakens it. At times, the cuticle layer doesn't get re-flattened properly leading to a damaged strand of hair.
Furthermore, not only is the cuticle layer lifted to let the relaxer in but the very bonds that give your hair its kinks, curls and coils are permanently changed further weakening each strand.
If you then braid your hair you're braiding hair who's protein infrastructure has been compromised. The likelihood of incurring hair breakage is a lot higher than when you braid natural hair. Really, if you prefer to have relaxed hair you should avoid braids. Relaxed hair needs constant refortification with protein conditioners to keep it strong. If you braid your hair you're much more likely to forget to do this and to neglect the hair beneath.
When can you braid your hair again if you really want to?
I would say wait until two months have passed or when you have about an inch of new hair growth before you get extensions. Your new growth won't have been relaxed and will be stronger - the protein infrastructure will be intact.
Have you mixed relaxer with braiding and had dire consequences as a result? Tell me, please!