Switching to formula

My sweet girl is still not back up to her birth weight and she’s a month old. We started out nursing only and she did great nursing. We she wasn’t up to her discharge weight after 2 weeks, so we supplemented with formula. When that didn’t work, we switched fully to formula and I pumped to keep my supply hoping we could go back to nursing. 3 days after the last appointment we did a weight check and she finally gained 7 ounces. They told me I could go back to nursing and giving a bottle every other feeding. Went back for our one month appointment and she had lost weight again. I just want my sweet girl growing and staying healthy but it’s really hard for me to give up the breast milk. I made it nursing my first daughter for 6 months. I know it’s not helping her thrive (they think it’s the fat content of my milk because I do not have a “fat cap” when I pump and I’ve tried adding foods that could help to my diet), but I feel like I’m failing her giving it up. I know the antibodies in milk probably have a lot to do with why my oldest has never really been sick. She’s 3 and has only ever had strep. I just don’t want to be the reason my youngest is sick. Any other moms have a similar situation?