Not long to go!
I didn't lose hypo awareness, but the level at which I would "feel" low blood sugar definitely decreased - particularly in the later months of my pregnancy. I think it is natural when control improves (rather than being pregnancy related), and it has continued to some extent post-birth as my control has stayed pretty good. The only solution for me was frequent testing - I dread to think how many test strips I got through!
Looking at my basal profile from just before I delivered, my overnight basal rates are a lot lower than my daytime rates (bigger difference than when not pregnant) and I didn't need to adjust for dawn phenomenon (which I do when not pregnant). Basically, I was taking much lower levels of basal insulin overnight and quite a lot more during the day, which sounds like it might be a similar pattern to what you're seeing?
Can you perhaps adjust your basal insulin (if pumping) or long-acting insulin (if MDI) to better match your requirements and see if that works?
Also, if you're anything like me, you'll probably find that you've no sooner figured it out than your requirements change again. It felt like I was constantly "course correcting" as I went through pregnancy! All worth it, though.