Is it possible that botox for underarm sweating does not work for some people?

Only a very small proportion of patients will not find Botox effective for armpit sweating (axilllary hyperhidrosis). A higher dose might be necessary in your case and your doctor might consider doing 100 units per each armpit for a total of 200 units. 

Injecting Botox for axillary hyperhidrosis requires skill. It is simply not just injections. You must inject in the proper area after a starch/iodine test. Also the injections must be placed at the proper depth or they won't be effective. I have found only one person in 10 years that didn't respond after she had multiple prior treatments. My guess was that she was developing antibodies and she responded better with Xeomin.