Why must IV/key-pairs not be reused in CTR mode?
Yes, the attacker would have a realistic chance of recovering plaintext, and preventing him from knowing the IV values does not reduce this risk.

The problem is that CTR mode encryption is effectively:

$C = P \oplus F(Key, IV)$

where $P$ is the plaintext, $C$ is the ciphertext, and $F$ is a complex function of its two inputs.

The problem with this is if you encrypt two different plaintexts with the same $Key$, $IV$ values, then the attacker gets two pairs:

$C_1 = P_1 \oplus F(Key, IV)$

$C_2 = P_2 \oplus F(Key, IV)$

Where he can see the values $C_1$, $C_2$.  With those, he can then compute:

$C_1 \oplus C_2 = P_1 \oplus P_2$

and thus deriving the value of the two plaintexts exclusive-or'ed together.

As for how that can be attacked, well, you can find two examples against ASCII-English plaintexts here and here.

And, note that since the attacker didn't actually use the IV value, it doesn't matter to him whether he knows it or not.