Qg's suggestion is a good one and what I'd do. Even on small wheels the area of tyre that needs to be inspected is huge; the tread is over 1.25m long, and narrowing down the area where there might be something stuck in the tyre is a good move.
It is also possible for the tube to get pinched or the valve to be defective. If you have the twinwall Brompton rims you need to use good quality rim tape (eg velox); tapes that are thin, stretchy, or can moved around can give you incessant punctures.
cheers