You can raise it back up again after the drop.
In this edition, even if your magic hits 0 you can raise it back up again.
Actually, on page 167 of CRB
..your maximum Magic rank increases. Your
maximum Magic rank is 6 + Initiate Grade (reduced
by one for every full point of Essence lost)...
So, Essence lost does reduce your maximum magic rank, not just your current magic.
If you haven't initiated and you drop your essence to 0.x, you can't raise your magic. One could argue that you could still try to initiate, but I don't know how that would be possible with a current magic maximum of 0.
Now, if you had initiated at least once, you could raise it back up to 1.
I have a strong suspicion of change blindness involved with the essence and magic sections of book. Would be surprised if they don't eventually release Errata to be more precise and establish full burn out rules (0 and done, no more opportunities regardless of initiate grade). If not Errata, maybe in the Street Wyrd magic book, hopefully.