My third DS threw up 2-3 times a week or more for a few months when he was a preschooler. We couldn't figure it out! The dr eventually thought it might be neurological and ordered an MRI, but my instincts told me it was more emotional/psychological, related to anxiety and sensory issues. He had started with a new babysitter who strongly encouraged him to eat his vegetables. Being a compliant kid, he'd squirrel them in his cheeks until I picked him up. Eww. He would sometimes vomit at her house, but actually more often it would be in the middle of the night, hours after the offending food was spit out. Once I discovered what was happening I decided to send him with a lunch from home everyday - healthy food that I knew he liked. Vomiting went away, overnight! Almost a year later, the first week of Kindergarten, the vomiting returned. I found out the teachers made the kids take one bite of everything on their tray before could go to recess. Once I let them know that really won't work for DS and why, no more vomiting. And we would check the menu carefully and sent lunches on days where the cafeteria food choices wouldn't work for him. DS has powerfully sensitive senses, his sense of taste and smell are way keener than mine, and I think offensive tastes, smells, and textures truly overwhelmed his neurological system and his body responded in a reasonable way - to get that stuff out! So I guess in a way the dr was right, it was neurological...just nothing that would show up on an MRI!
I don't know if anything in my story rings true for your son, but if he has sensory issues, picky eating, anxiety, difficulty with transitions....I'd keep that in mind. Good luck finding your answer!