What would happen if the last message in a three-pass authentication protocol was undelivered?
The three-pass authentication protocol defined in ISO/IEC 9798-2 at 5.2.2. and it is defined as follows;


$\text{B}$ generated random $R_B$ and sends to $\text{A}$;
$$\text{B}\xrightarrow{R_B\|\text{Text1}}\text{A}$$
$\text{A}$ generated random $R_A$ and sends to $\text{B}$;
$$\text{B} \xleftarrow{\text{TokenAB}\;=\;\text{Text3}\|eK_{AB}(R_A\|R_B\|B\|\text{Text2})} \text{A}$$  
$\text{B}$ generated random $R_A$ and sends to $\text{A}$;
$$\text{B}\xrightarrow{\text{TokenBA}\;=\; \text{Text5}\|eK_{AB}(R_B\|R_A\|\text{Text4})} \text{A}$$
$eK_{AB}$ is the encryption with the $K_{AB}$;



  What would happen if the last message in a three-pass authentication protocol was undelivered?


Whoever started the protocol, $\text{A}$ connects to $\text{B}$ by $\text{tokenAB}$.


If $\text{B}$ started then $\text{B}$ can send back the $\text{tokenBA}$ to $\text{A}$  for the agreement.
If $\text{B}$ doesn't send back the $\text{tokenBA}$, $\text{A}$ cannot decide it was actually $\text{B}$ or not. Since, anyone can send an $R_B\|\text{Text1}$ to $\text{A}$.




Old answer if the question was the Three-pass protocol of Shamir

It not verification of each other it is just message exchange.

From Wikipedia;


  In order for the encryption function and decryption function to be suitable for the three-pass protocol they must have the property that for any message $m$, any encryption key $e$ with corresponding decryption key $d$ and any independent encryption key $k$,  $$D(d,E(k,E(e,m))) = E(k,m)$$


i.e.

$$D(d,E(k,E(e,m))) = D(d,E(e,E(k,m))) = E(k,m).$$

If the third, i.e. the last, is not delivered, the messaged won't be decrypted. He will have $E(k,E(e,m)))$ in his hand, but he cannot decrypt this because he doesn't know the key $d$ of the sender.

The receiver can use the Commutativity property to reach $E(e,E(k,m))$ but this won't help,too