In support of Yehuda's answer, I would like to show that re-using a IV is very dangerous when it comes to encrypting private keys:
say that you are using CBC mode encryption: you would be able to distinguish between private keys that start with the same bytes. Usually the keys are encoded in some way. So it could be that e.g. 4 bytes are encrypted in the block. If you would find the same ciphertext block you would know that the 4 bytes of the two keys are identical;
if you are using CTR mode then the situation becomes worse: you could XOR to see which bits are identical or not. If party A would expose the private exponent somehow then the key of party B would become compromised as well. If party A knows the value of his own private key (not a given when e.g. a hardware device is used) then it also can decrypt the private key of party B.
A synthetic-IV mode (deterministic encryption) would work better as it let the IV on the entire plaintext. That way you can only distinguish exact duplicates.
So you should use a wrapping mode that allows for deterministic encryption. You should definitely make sure that the IV complies to the requirements of the mode of operation (CBC, CTR) to create a CPA secure cipher.