I think there is a possibility that is indirectly supported by the reboot movie. In this movie Alex, the player who entered the game in 1996, describes himself as having been in the game for "a couple months". The assumption of the other players and the audience is that the game distorts time, making Alex believe he has been in the game for only a few months despite decades having passed.
But the idea that they just got lucky and encountered Alex on his last life in a lethal win-or-die scenario doesn't feel quite right. While it is at times scary and violent for the players, Jumanji never really feels malicious or like its goal is to kill them. Violence is often cartoon-like, such as when Spencer/Dr. Bravestone punches henchmen and they fly up into the air or when Fridge literally explodes just from eating cake.
And speaking of, despite numerous horrible deaths that would be emotionally scarring to experience like being eaten alive, trampled to death, or being shot in the chest, none of the players exhibit the signs of trauma they would almost inevitably have if they lived thru those events in "real life". Their injuries are short-lived of course, they simply pop back into existence fully healed, so that might explain it. But victims of torture, even if they never suffer physical injuries, often remain scarred for life by it. Emotional trauma can be just as destructive as physical trauma.
One way to explain how they emerge unscathed could be to assume that the horror of dying in the game is somehow muted. You remember what happened to you, but in a more subdued way. This again would fit with the idea of a game: the goal is to give players enough feedback to know that what happened was negative, but not so much as to overwhelm them.
Over and over when Jumanji makes an environmental choice it selects less onerous ones; players aren't saddled with desperate thirst or hunger, disease or crippling injury. They aren't even saddled with mundane requisites like performing work to earn money to get food and shelter. It seems that Jumanji is less malicious and more like a hyper-realistic game environment where only aspects of reality connected to puzzle solving, bravery, and excitement are fully depicted. So would permanently killing players who run out of lives fit the theme everywhere else?
And along those same lines, would it make sense to have to create some weird distorted flow of time to make in-game player's perceived time only a matter of weeks compared to newly entering players when the game has no way of knowing whether new players will arrive in an hour or in a century? How would you even design a time speed under those conditions?
But there is another possibility that matches the idea of a game. And that is that when a player runs out of lives it simply restarts the game. You lose, try again.
But even if you did get to just start again, enough repitition would eventually become a kind of hell where you were trapped in an endless loop. Why expose players to this when you've taken such pains elsewhere to avoid those negative aspects?
So instead, when a player loses and the game resets, why not wipe their memory along with everything else. Because the magic of Jumanji allows it to send the players back to the real world right after they left you could play as long as it took and only remember the last iteration where you finally succeeded, which also seems a lot more fun for players.
In the movie Alex remembers dying twice, but also seems to have a knowledge of a whole bunch of lethal traps and dangers that is never really explained. Maybe he just got incredibly lucky and managed to avoid all mosquitoes, flying spears, saw blades, henchmen, and god knows what else the first time he encountered them, but it seems to me that he also might just have died an enormous number of times and developed a kind of muscle memory about dangers he previously encountered that he interpreted as intuition or luck.
That's my guess, anyway. To me, it seems to fit the theme of other things in Jumanji. If you lose your last life while there are other players still in the game maybe you pop back in the game without any memories from before, or maybe you stay dead until the other players either die or win the game and leave. Heck, for all we know maybe the new players all died a couple of times before making it far enough to encounter Alex and we are only seeing their last run-through! Obviously this is all speculation, but to me it does seem to kind of fit what we do know. Maybe we'll find out for sure in the next movie.