One-Time Pad Distribution of Keys Between Two Parties
Let's say Alice and Bob have $c$ bits of pre-shared secret key material.  Alice generates $a$ bits of new key material, concatenates it to a message $M$ that is $b$ bits long, and uses $a+b$ bits of their pre-shared key material to encrypt "message||new-key".  She sends this secure message to Bob, who decrypts it with the shared key.  Now they both have $a$ bits of new shared key-material, but in order to securely send those $a$ bits and the $b$ bit message $M$ they had to burn through $a+b$ bits of the previous key material.  The total key material they now have to encrypt future messages is:

$c-$ (Amount spent to send "message||new-key") + $a$.  

The term (Amount spent to send "message||new-key") = $a+b$, so the amount they have left is:

$c-(a+b)+a$,

$= c-a-b+a$,

$= c-b$.

So they are no better off now than if Alice had simply send the $b$ bit message $M$ alone without an appended new key.