In short, it was just too difficult to balance, so it was omitted
When asked over twitter, Mike Mearls responded:
Real headache to balance - tried a few designs, none worked well. Tabled for now.
But what does that mean?
Mearls doesn't really go into any detail, so it's difficult to say exactly what he means by "headache to balance". The only thing we can say with any certainty is that WoTC tried to make a 5e version of Permanency. And after testing several models for the spell, they decided that each of them had some flaw that made the spell unfit for inclusion in the PHB. And so, they decided to release the game without it.
Since then, they either haven't put in any more work with the spell, or they haven't managed to make another version that met their benchmarks for public release yet.