Security of a cipher with some imperfection in round function
If an all-zeroes block creates all-zeroes for every key that's definitely an issue. It's not necessarily likely to be serious, but could leak data about the plaintext and does not qualify as a secure block cipher.
However, the solution is fairly simple... simply XOR one of k1 or k2 with a constant value to turn your all-zero block into something that'll produce a better result. Personally I'd XOR with the current round number in each round because that'll prevent your algorithm from accidentally ending up with another input that produces the same issue.