I suggest you head over to realbakingwithrose.com for sourdough questions and info. The bakers over there are very experienced. Taking into account my knowledge and experience with sourdough, I would say you are using the wrong process to make the bread. You make the culture first, get it going good and strong (5+ days of feeding, dividing, feeding, etc), and then you make a sponge with a portion of the culture. The sponge has to sit and activate for a good 24 hours before you make the actual dough. If the dough has not risen in 24 hours, the sponge, and possibly the culture is just not strong enough yet. If you’re not using a formula/recipe, then you could also not be using enough culture in the dough. Once you add commercial yeast to a sourdough, it’s not sourdough anymore. The commercial yeast will take over and push out/kill the wild yeast, and the desired characteristics of sourdough are lost. Done properly and when the wild yeast are given enough time to do their thing, commercial yeast is never needed.
Each time you make a loaf of sourdough, you have to reactivate the starter with 5+ days of feeding at room temperature before making the sponge. The yeast basically go dormant under refrigeration, so you have wake them up and get them vigorous and active before making the sponge for the loaf.