How can my mom in the States obtain a new birth certificate after losing it in a hurricane?

Good question…

Unless it is for a minor, most countries require the applicant to apply for their own documentation. If a third party is making the request, additional requirements prevail.

Start with the embassy near you and at least look online

At her birth place , with power of attorney anyone can request a copy. I assumed she speaks Thai? Have her contact me I’ll walk her through. No charge, just a Thai helping another Thai.

Nowadays you can contact most of not all Thai government agencies via Facebook.

Has she lost her passport also

It will be hard to get a birth certificate especially since the Thai Embassy was no help. She may have to fly to Thailand and seek help from the office in the district she was born. I live with my Thai wife in Thailand. She didn't have a copy of her birth certificate and the office did not have one. So they gave her a bunch of paperwork her parents had to fill out and the Village Chief had to sign. I guess what I am saying is Thailand's bureaucracy is hard to deal with at times. Good luck.

Maybe in the amphoe where she was born?

BORA Web Portal

Thai embassy