Spring to fall is the breeding season. While they can have a litter every 28 days. The best research I am finding suggests they have 3 to 5 litters per year, with 1 to 8 kits (babies). By some estimates only half of the kits survive to leave the nest.
They reach sexual maturity in 3 to 4 months, so the surviving kits from the early part of the year, are likely parents by the end of summer.
I could not find any reference speaking to survival only in the summer, but several sources list the annual survival at 15 to 30 percent, with the eldest wild cotton tails being about 3 years old. Domesticated/captive rabbits have life spans similar to cats and dogs.
A single doe will have maybe 25 kits per year (conservative guess), of those a couple will be females from the first couple of litters, and they will have maybe 10 kits each before the end of the season. So a single doe begets maybe 45 rabbits in the season. Most of which do not survive.
The summer is a good time for rabbits lots of food, it also a good time for their predators, who are also making babies that need to be fed.
Rabbits are Crepuscular animals they are primarily active at twilight (dawn and dusk) I think there are multiple reasons you see fewer rabbits as the season extends. Clearly there is a lot of predation, but there also needs to be enough surviving rabbits at the end of the summer to feed the predators through the winter.
Lots of rabbits die young, and it is mostly the young rabbits you see running around in the spring. The mother rabbit has another litter she is tending to when you see these older youngsters running around. The rabbits that live the longest are the ones who stay to the shadows and/or are out at dawn and dusk when they have more survival advantages.
The rabbits you seen running around at day time are not the only rabbits in the area, but they are the most likely to be eaten the soonest.
A couple of references I found that are interesting.