Sorry but i'm going to commit necromancy on this post because there is a very good reason nobody has mentioned
"an immensely complex spell ... involving the magical concealment of a secret inside a living soul. The information is hidden inside the chosen person, or Secret-Keeper, and is henceforth impossible to find -- unless, of course, the Secret-Keeper chooses to divulge it." (PoA pg 205/152)
The key word here is 'a' as in singular from a language point of view. If he split his soul then every piece combined is the keeper so his main body would also have to be inside the charm to (and all the other pieces), he would have to be inside the charm himself with all the other pieces to work.
He cant carry out his mission by hiding inside the charm, the wording means that all the pieces are secret keepers combined so if even a single piece dies the spell is broken - you cant have a full cake with even 1% missing.
If the secret keeper dies the charm still remains intact if he hasn't told anyone, but the whole soul is needed for the charm to work, if one part dies he is both alive and dead at the same time and so the soul is no longer complete - which means the charm has to break (not be lost forever).
The spell is dependent on a complete soul that is either alive or dead, not in limbo with UK English the word 'a' changes everything. Its singular so no part could die without breaking it, it can only be hidden forever if all the pieces die (which defeats the point) or if ALL the pieces remain alive
This may not be what JK intended but she is usually good with the wording (her math may be bad, and she created some plot holes but her wording has always been literal and exact)
A spell can either work or fail but it never semi works, the closest we get is the cruciatus curse on Bellatrix, even that was due to him not really wanting to hurt her, the spell worked it just didn't have much strength as he didn't want to. The volume was dialed down but it did work