Is losing wudu during the prayer, and then continuing the prayer haraam?

Salam alaykum brothers, today when I was at the mosque, I lost my wudu during the prayer (2nd rakaat, while reciting Surah Al-Fatiha if I remember correctly), after that I was too embarrassed to just leave, I finished the surah contemplating whether I should stop and leave, I did rukoo partially thinking that I'd still get hasanat for doing it, and I did prostrations also partially thinking that I would get hasanat, I was doing sujood and then feared that what I'm doing is sinful, so I stood and left my salat without Salam. I say partially because the main reason was that I was too embarrassed to leave and I also showed little or no khushu, but Allah knows best. Also, my prayer was sunnah, does that change anything?