Ball also thinks the defending as a whole needs to improve.
Howard's performances have been under the spotlight for some time and there have been calls for Joel Robles to be given a run in the side ahead of him.
Ball wrote in his Liverpool Echo column: "How many more mistakes will Tim Howard be allowed to make?
"Look, he's not doing them on purpose. But as an ex-player, I know that if you're not playing well and the manager takes you to one side and says you're being dropped, you don't have any arguments.
"You just work hard in training and wait for your opportunity.
"Maybe that time should now come for Howard."
Ball was critical of Howard's role in Stoke City's equaliser on Monday which brought the scoreline back to 3-3 after Everton had hit the front for the first time in the game. The Potters ended up taking all three points following a penalty from Marko Arnautovic.
There was a point when Howard even sarcastically applauded the Gwladys Street end of the ground as he seemed to respond to criticism from them.
But Ball has pointed out that the side's defending in general hasn't been very good, and even though he thinks there may need to be a change in goalkeeper, the players in front of him need to do their share, and tighten up.
"Everton know the goalkeeper isn't the best at protecting his six-yard box, so the defenders have to work harder at preventing the crosses coming in.
"We are too busy thinking about the next pass or one-two sometimes instead of just clearing the ball."
That would mean a change in the mentality of Martinez when it comes to his style of play as he likes to play the ball out from the back, but maybe there is a case for the side to do the basic defending and think more about the style at the opposite end of the field - where the side is doing very well in front of goal.
As far as Howard is concerned, there have been times when Robles has come into the side - notably in the League Cup - and performed pretty well but has never been allowed to keep his place, suggesting that Martinez is determined to keep the American as his number one.
But there is only for so long that a player's form can come under fire before they have to make way.