If you are getting allot
503 FetchError c no backend connection error and you enabled Saint mode than you have to add following to your backend.
.saintmode_threshold = 0;
Option "saintmode_threshold" tells Varnish how ,any items can be vlacklisted by saint mode before it makes your backend sick. Is setting saintmode threshold to 0 still produces "no backend errors" try sett try setting it to a very high number.
To check if you have such error use following command
# varnishlog -c -m TxStatus:503 | grep FetchError