Repeat BRUE x Reflux?

Hello. My son (4mo) has had 2 BRUE events now in the past month. We have gotten every work up possible done in the hospital (MRI, ultrasound, EKG, echo, 48hr EEG, bloodwork, etc)

Doctors are stumped and the only thing we can think of is he did come up positive for dairy allergy in his stool sample which could lead to reflux and causing the BRUE like event. If this happens again the doctor told us we are tapped out and will need to go to a research hospital.

I am wondering if anyone has ever experienced anything like this? For context each BRUE event he briefly turned pale / limp for about 30-60 seconds before we noticed and stimulated him. He never truly lost consciousness either time.

Just looking for ANYTHING related or positive.