I sent in a DQ6 for the same endless power-cycle death. There's one possible solution, but it may not work for all boards. DQ6 has dual bioses and resetting in a short succession or shutting it down immediately may cause the bios to think it's a corrupt bios so that it will recover from that. It doesn't work for everyone.
I think DS3 series is single bios so the bios may be corrupt. Gigabyte solders the bios on the board so we can't swap it out. RMA is the only solution. FWIW, DFI uses user-serviceable bios chips.