As long as clover is established and you have 3" of rain per month - then you almost cannot mow too much.
Clover itself - does not need to be mowed until 3/4 of the crop is in seed. Be aware that the closer you get to fall - more will go to seed - its JUST WHAT IT WANTS TO DO. Mowing will delay clover going to seed - but as the daylight hour shorten - the plant "hurrys up" and goes to seed.
Mowing revitalizes the clover - but the main reason for mowing is to help inhibit annual weed growth. By fall - it doesn't matter much - becase the competing annual plants that you mowed cannot go to seed before a frost. The clover plot willl come in stonger than ever the next spring.
Grasses are the limiting factor - and mowing them only makes them stronger as well (like your lawn) -
When grasses are the largest competition - you either re-plant - or spray in a nutshell.
FH