I have dealt with these a lot before when I had less patience and practice setting up for bends, etc... and the key is in the tiller. If it truly isn't hinging, you are good.
If it is, you can saw a kerf right there and jam a patch in with glue. If it's the result of a bigger soft spot that's tougher.
OR, you can tie on a stiffening patch to the front. Get a scrap of osage with a chased ring for a back, about 2-1/2" long and 1/8" thick or so, and heat bend it into a shallow "U" shape. Bevel the edges so it will blend in, spot glue it to the back of the bow, and tie it down with sinew or fine twine so tightly you pull the "U" out of the patch. Don't glue it. Doesn't seem like much, but if the hingey spot is 1/100 of an inch too thin, 1/8 of an inch will stiffen it a good bit.