1,000 watts is thrown around loosley around here so let me see if i can help.
1,000 watts= 1.32 HP, 44,240 ft-lb/min, 56.9 btu/min.
Long story short, upgrade to 2 or 0 gauge wire and the problem will go away. Your amp at high volume is basicaly choking trying to pull current through the cable. Bigger wire equals less resistance (heat).