Ink and fount. Is it all colors or just magenta? Magenta usually shows any defects in chemistry first.
First, check with the pre press dept. to see if their chemistry is up to snuff. Try developing and gumming a set of plates by hand to eliminate this variable.
Then try keeping current fount and switch ink brands. If it still happens check fount mixture. Some founts are buffered and may read a normal PH level but could be overdosed and breaking down the ink. The alcohol sub can also cause this problem. One step or two step fount?Try reducing the sub and remixing the fount with small amounts of fountain concentrate, checking and adding until the desired PH level is reached.
Water temp and roller temp play a big part also. Do you have chilled rollers? If not, no matter what you do you are fighting a losing battle.
Ink tack and flow can also be a culprit with higher press speeds. Try a higher tack or heavier body ink.
Before you try anything, the press rollers should be washed with a calcium remover.
I am also assuming the plates and blankets are packed properly and the rollers are set and in good shape.