Well, first of all - try to determine if this is the case. If you install the tube/tire with valve straight up you can then see if braking causes it to tilt or not. If it stays straight, then your tire isn't slipping on the rim.
If it does slip there are two options apart from increasing pressure.
1) put a thin layer of liquisole on the bead of the tire. This usually will increase the friction enough to keep the tire from slipping and can be really useful particularly on folding tires.
2) the hardcore-no nonsense approach is to use contact cement or tubular glue on the bead on one side of the tire. You only need one side "open" to be able to get the tube out, so although it sounds drastic the consequences are quite manageable . Tubular glue will keep the tire from slipping and it's weak enough that removing the tire when that day comes isn't too much of a chore.