This is the first I've heard of this problem. Tunnelblick itself doesn't have much to do with the VPN traffic; OpenVPN does all that.
So it could be something with OpenVPN, or something with Mavericks. Or could it be you are now using a different network (a wireless network, for example -- my understanding is that they sometimes cause replays).
Or -- unlikely -- maybe it really is a replay attack!
Perhaps you are using a different version of OpenVPN since you upgraded. Try changing the OpenVPN version on the Settings tab. (First select the configuration(s) whose setting(s) you want to change in the list on the left, then change it in the drop-down menu).
If that doesn't help, you probably should ask -- or have your IT department ask -- some OpenVPN experts for help:
I'd appreciate it if you let us know how you resolve the situation.