In the 20-verse (nijûin 二十韻) renku that this website features,
spring and autumn sections have three verses apiece,
while summer and winter only have two.
In the general rules of renku, spring and autumn verses can appear in clusters of 3-5 verses;
summer and winter can appear only in sequences of 1-2.
This is not arbitrary.
From ancient times in Japan,
spring has meant rice-planting. Festivals at Shinto shrines throughout the land celebrate spring.
People gather to pray to the gods for good crops.
When cherry blossoms bloom, the soil is warm and ready for seeds.
So, spring is a very big deal.
Later in the year, autumn means harvest.
The rice is ready for reaping.
Once again people gather at shrines, this time to thank the gods.
(Sumo tournaments, by the way, evolved as a sacred harvest ritual.)
Poets gather under the harvest moon to celebrate the culmination of the agricultural year.
So autumn is a very big deal too.
Summer and winter get fewer verses in renku because,
in terms of the seed-to-harvest cycle of farming in the agricultural year,
they are less significant, in-between seasons.
Renku (and its offspring, haiku) celebrates the Great Cycle of spring to autumn:
blossoms to moon.
...which answers another question:
Why are blossom verses and moon verses built into every renku?
Because renku reflects and celebrates the Great Cycle of Life: planted seed to harvested grain, cherry blossoms to harvest moon.