I'm sorry to see you're having issues with your BT sport channels on Sky. The BT Sport and ESPN channels are all broadcast in the same signal range and if your dish is slightly out of alignment it could cause signal reception problems. Check out this link No signal for a more detailed explanation.
This has been reported many times on this forum and it's usually a case of the dish being slightly out of alignment. The best way to check is try Men & Motors, (they use the same transponder as BT Sport). If you see the same issues it's your dish.