For me the definition of roguelike is a game that uses the interplay between permadeath and procedural content to create interesting player decisions. Understanding that interplay is the main challenge in designing a roguelike.
I try to solve it by creating 'common rare occurrences'. Like in KlingonRL you can happen upon a system with no gas giants (low fuel), Romulans, Space Whales, Tons of Pirates, No Pirates, Starbases or None. You'll never see everything in one game. You might not ever see the Romulans. But the point is that even if you die, it's no biggie because the next game will be all new challenges.
The other main design challenge is making it so the character knows why they died so they can adjust for next time. Eventually a player will play enough that they know how to beat enough of the challenges they can beat the game. Thus achieving mastery.
Other permadeath genres solve the issue in other ways. Arcade games might have multiple lives, but they have permafailure too. No saving in an arcade game. They solve this issue by making the game EXACTLY the same each time so that a player can hone their skills to superhuman precision.
Strategy games have permafailure as well, but most commonly they allow saving and reloading. It is common, however, to play a game on Hardcore and not allow reloading. Play Battle for Wesnoth this way and watch your play experience deepen to fantastic levels. Make sure you put it on easy mode though, that game is brutal.
Understanding that's how the game is designed and appreciating it is a challenge for many (most) players.
Making all of that stuff actually fun is another thing altogether.
So to the question of a roguelike without Permadeath, what you are really asking for is a hybrid. An RPG with procedural content. That can still be a fun game, but it will not have the core trait that makes a roguelike interesting. It can, however, have that core trait that makes an RPG interesting. Which is the ability to develop a character to fantastic levels without having to worry about losing. You just can't lose in an RPG, kinda stress free.
BTW if you are looking to go the other way, to keep permadeath but ditch procedural content, then you are in luck. Any RPG can be played in this way. Any game can, really. There was a dude that played Far Cry that way.
