Could it be the "Yubi" series of portulaca? There's also the Tequila and Sundial series. Yubi is supposed to trail more and have broader leaves and larger flowers.

The more heat and sun the better for all varieties - the more sun the longer the flowers stay open.

The Sundial portulaca "stay open longer in the day than other Portulacas", but they don't claim them to stay open all day.

I don't think any of the portulaca types will stay open all day under all conditions. Whatever type I find as seedlings and plant in a retaining wall planter reacts to the amount of sun they get - overcast/cloudy/nightfall and the flowers close.

I thought the Yubi series was new but I don't think there are any claims it overcomes unfavorable light conditions and stays open sun up to sun down all season.

Swallowtail Garden Seeds has a variety called 'Sunseeker' that they say stays open morning 'til sunset.

The only way Sunseeker will stay open all day, is it it is sunny out - just like all other portulaca, and Gazania.