First of all, thank Steve for taking the time to look at this.
9c:af:ca:64:2c:42 is the vlan10 interface on the 3750
00:1c:f6:1d:4c:11 is the 3845 router interface on vlan10.
The capture was taken in the scenario with the two routers in the mix (the diagram before last). So the frame from the workstation to the server has the source MAC of the 3845.
If I take the routers out of the mix, the capture still looks the same.
"This makes me believe the client isn't sending the ACK the server is looking for, so it retransmits. It's not like I see anything additional sent from the client capture and it's retransmitting anyway. Unless I'm missing something." >> Yup, that's the strange behavior, even though the workstation sends the ACK, once and the server receives it, the server keeps retransmitting and the workstation never ACKs on any of the subsequent packets.