6.5 Update 6 and can be true with the other version also.
Below is the Error in the replication log file:
However, the replication seems to be working fine from Store to Enterprise and vice-versa.
As per the error in the log file, it seems there can be a connectivity issue between Enterprise and Store.
This means, when the replication service tries to push the data, it does not get a live connection with other servers hence the above error gets logged in the replication log file.
However, the replication service starts working as soon the connection gets established between Store and Enterprise.
As per confirmation from the customer that replication is working fine hence there is no issue but to ignore such errors, the connection between stores and enterprise should be in good conditions.