refrigeration effect on dough strength?

I've been enjoying this site as a super helpful resource for the past months as I've been trying to improve my technique, and recently started to get quite pleased with reasonably consistent results. My goal is always a tasty sourdough bread French style, my basic method is about 50/50 all-purpose and wholewheat, with some rye instead of wholewheat sometimes (5 to 10%) and I always aim for 70% saturation. I usually start with 200g flour & 160g water with a spoonful from my starter on the morning or early afternoon of day 1, then next morning autolyse 500g flour with remaining water (to achieve 70% hydration) and mix in the 360g of starter plus salt. After initial kneading I occasionally stretch & fold and in the evening divide the dough in 2, shaping one half into a ball, proofing in a basket and baking in a dutch oven. This bread usually comes out very satisfactory in terms of shape (dough strength) and crumb.

But now for my question: I pop the second half back in the bowl, and refrigerate it, with the goal of shaping proofing and baking it 24 hours later. I find the taste of this second loaf is better than the first, more sour with more interesting taste. However, I usually don't get the same tension at the shaping phase and a less shapely bread with slightly less open crumb. I've noticed that while in the fridge, if it's come up and I do a stretch&fold (usually after 8 or 12 hours), the dough strongly deflates. The dough also feels "rougher" than pre-refrigeration, as if it's got less strength to hold air. I do allow it to warm fully to room temperature before shaping, but find that I'm less successful in building up tension.

Any ideas on what might be causing this "texture-change" to the dough? Should I not touch the dough while in the fridge? (i.e. no stretch&fold?) Is there something else I should be doing or not doing?

Below is my result from this Monday, which was the non-refrigerated version. It's 24-hour later brother was much flatter, though tastier!