If you still getting the problem and it is a wooden recorder, there is one other possibility. If the recorder is secondhand, it is possible that the previous owner was not careful enough when oiling it and got oil on the parts of the block that are supposed to absorb moisture. They could have also handled it incorrectly and got greasy fingers over it.
If this is the case it may be necessary to remove the block and treat it a couple of times with isopropyl alcohol. This will leach the oil out and the block will go back to doing its job of absorbing moisture.