Walters' spot-kick was saved by Mark Schwarzer in last Saturday's 1-0 Premier League defeat at Fulham and in January he struck one against the bar in a 4-0 top-flight loss at home to Chelsea that also saw him score two own goals.
Pulis has not stated whether he does or does not want the Republic of Ireland international to continue taking Stoke's penalties but he certainly feels Walters deserves credit for volunteering, and has suggested that if the 29-year-old does so again in Saturday's home league clash with West Ham - and none of his team-mates do - then he is happy to let him proceed.
Asked if he thought Walters should retain spot-kick duties, Pulis said: "People have asked me that, and people say 'we would get him to take it, or we would get him to take it'.
"That's all fine, but do those players really want to take it when the game is going on? Jon picked that ball up (in the Fulham match) and there was no doubt about it - he wanted to take the penalty.
"He missed it, and as I have said before, people do things in life sometimes that are not right, or do not go the way they or you want them to go. But that is life, and you have to get on with it.
"You have to make sure you back the players who are prepared to do it.
"If we get a penalty on Saturday and Jon picks the ball up and wants to take it - and there is nine or 10 others who don't - then let Jon take it."
Stoke, currently 10th, take on a 14th-placed West Ham side who will go level on points with them if they can secure victory at the Britannia Stadium.
That would halt a winless run of eight away league games for the Hammers, a sequence in which they have suffered seven losses.
Given that Stoke have been beaten on their own turf only once in the league all season, it looks like a long shot, but if the London outfit are to upset the form guide, their towering frontman Andy Carroll - on loan for the campaign from Liverpool - could be key.
In the absence of suspended centre-back Robert Huth, the Potters are set to move either Marc Wilson or Geoff Cameron, both of whom usually play at full-back, into the middle of defence to partner skipper Ryan Shawcross.
That may work to Carroll's advantage, although Pulis is keen to play down any such suggestion.
Regarding the defensive situation, Pulis said: "We have Marc Wilson, who has played centre-half before, and Geoff Cameron, who has played for the United States at that position, so we have got cover there.
"We have got Shawcross there as well, and I don't think it will be determined by that single battle (with Carroll), whichever way you look at it."
Huth begins a three-match ban after earlier this week accepting a violent conduct charge from the Football Association relating to an incident in the Fulham game, where he caught Philippe Senderos in the face with his forearm.
Midfielder Steven Nzonzi will be wearing a protective face mask if he features having broken his nose in the contest at Craven Cottage, while winger Matthew Etherington (back) and striker Michael Owen (thigh) will undergo late fitness tests.