Although the Whale speaks of the Runeys resting in Winter and a friend of mine stored all his Runeys throughout Winter, letting them out of storage again in Spring, healthy Runey Distribution in Winter is essential if you wish to have Crops growing and thriving in the Dungeons. The player who took all his Runeys off the Map during Winter did not have Crops growing in the dungeons at that point in the game.
Healthy Runey Distribution, therefore, is vital in all four seasons. If the Crops that you have sown in the Dungeons do not grow or actually wither, it is because of poor Runey Distribution.
A player left a comment to the effect that all his/her Runeys died and therefore the game was 'lost'. This is NOT the case. Players have been in that situation before and have recovered. It takes time but it is possible. There is not time limit to Rune Factory Frontier and growing Crops is only one aspect of the game. It is a vital aspect but there can be recovery in time from the total devastation caused by Runey losses.
I never had any dead zones personally but many players have and by working patiently to restore each District, one at a time, they were able to recover the ability to grow Crops both on their field and in the dungeons. The game WILL deposit Runeys on the Map each week, even in Winter. The only district where no Runeys will be deposited in Winter is the Homestead as Runey Distribution there is based on your own farming efforts and you cannot grow Crops in your field in Winter.