I have had the same issues trying to sign up for excursions starting with the roll-out of the "new" website - it is so frustrating! We were on a cruise in Europe when the excursions opened up for our WC, and after spending hours, I lost everything! I finally had to contact Linda to help me - I thought maybe it was just the ships WiFi. But then the same thing happened when I was signing up for excursion for our March 2021 voyage (which probably won't happen anyway). I stayed up and started the process as soon as they open at 11:00pm CT - slow as molasses! It was probably 3:00am before I got them all done (about 35 excursions). But I did learn from previous experiences to checkout about 3 or 4 excursions to be sure they were saved.
This has definitely been a problem for a while - lots of people post about it on the Regent Facebook site.