Small Offshoots on Tomato Plants Dying?

My tomatoes are producing well, but a lot of the smaller vines coming off the main stems seem to be drying up and dying where they come off the larger vine. I have been pruning them away, but it just continues.

I feed them Miracle Gro Tomato plant food every 2 weeks and I have no problem with the blossoms setting and growing just the smaller stems drying up and turning brown.
I have the tomato plants growing in oak barrel halves and used potting soil to grow them in.

By Debbie R