Several bits of evidence point to the fact that Fortnite will be keeping a no-build mode in the game permanently.
Fortnite's latest season, awkwardly themed around Resistance, launched last week and changed the game significantly. Not only did it add sprinting and mantling, but it also completely removed building from the main Battle Royale mode for a limited amount of time. Although it's still not clear how long building will be gone for, it seems that Epic will be keeping it in the game as a separate mode.
As pointed out by reliable Fortnite leaker Hypex, there are a few signs within Fortnite currently that indicate that some kind of permanent no-building mode will be added to the game in the future. Hypex points out that there are, "SEPARATE No-Building modes that they can enable ANYTIME after this limited time event ends". This has been leaked plenty of times over the past few seasons of Fortnite, which means it's likely that Epic will either keep bringing it back as a limited-time mode, or just have it be permanent.
The next bit of evidence is found in the loading screen following the latest update. The loading screen tips will now say "In modes with building enabled", which implies that there will soon be a range of modes that either let you build or remove the feature entirely. These two bits of evidence make it clear that no-building wasn't just a gimmick for the season's opening and will likely add it to the game's roster of modes.
This has been met with a mixed reception from the community. On the one hand, Resistance has easily been Fortnite's most popular season in some time thanks to the removal of building, so it makes sense for it be kept for the players who don't want to bother with it. On the other hand, some players are complaining that adding a no-build mode will split the playerbase even more than usual and likely lead to less interest in the base battle royale mode.