The friction (on ours) is done by two little ears pressing against the inside of the plastic that rolls with the blinds. It is possible to make those ears push harder by winding a stubby woodscrew into the hole between them (been there, done that, etc).
If you feel brave enough, take the blind down and pull the winding mechanism out of the cardboard tube. Then have a look at it, see if the woodscrew bodge will work on yours.
There may be a plastic collar left inside the cardboard tube, very difficult to shift, and I left it well alone.
Getting the winding mechanism to re-enter that plastic collar is helped by filing a chamfer on the front edge of the mechanism.