Please don't feel embarassed by asking questions that might help your brother's condition. It takes a truly caring sister to investigation this problem, since it is of a sensative nature.
It could be that your brother's blood pressure is spiking during this "activity", which would not show up on any test run by a doctor (unless the doctor was testing his right during the activity, which is ridiculous to think about). The closest test the doctor could do would be a stress test, the treadmill thing, and see how his blood pressure reacts under that kind of activity.
For a long time, one of my PCP's, quite a few years ago, thought this was happening to me. She thought my blood pressure might be spiking when I had a migraine(although my migraines didn't happen at any particular time). I tried a several different blood pressure medications which have been successful for a lot of people. Unfortunately, they didn't work for me, but they could be a good fit for your brother.
Hope this was helpful. Let us know how things turn out.