No, the client machine and esx server are not on the same subnet. They are not even in the same country. The datastore is on a different subnet as well, but it's on the same router. Putting all of the machines on the same subnet is not a viable solution for us. Does VIX require all clients, esx servers, and datastores to be on the same subnet? Here is the log files:

vmware-vix:
Oct 25 23:58:12.178: app-2268| Log for Vix pid=5804 version=-1 build=build-368992 option=Release
Oct 25 23:58:12.178: app-2268| The process is 32-bit.
Oct 25 23:58:12.178: app-2268| Host codepage=windows-1252 encoding=windows-1252
Oct 25 23:58:12.178: app-2268| Foundry Init: setting up global state (0 threads)
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: vixLogLevel = 0
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: vixApiTraceLevel = 0
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: vixDebugPanicOnVixAssert = 0
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: vixLogRefcountOnFinalRelease = 0
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: asyncOpWarningThreshold = 1000000
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: enableSyncOpSelection = FALSE
Oct 25 23:58:12.178: app-2268| Vix_InitializeGlobalState: enableExternalThreadInterface = TRUE
Oct 25 23:58:12.178: app-2268| LOCALE windows-1252 -> NULL User=409 System=409
Oct 25 23:58:12.178: app-2268| VixHost_ConnectEx: version -1, hostType 5, hostName https://<myip>/sdk, hostPort 0, options 528
Oct 25 23:58:12.178: app-2268| HOSTINFO 28779581451581 @ 2864716Hz -> 0 @ 1000000Hz
Oct 25 23:58:12.178: app-2268| HOSTINFO ((x * 2998529205) >> 33) + -10046224981807
Oct 25 23:58:12.178: app-4696| HOSTINFO 28779581451665 @ 2864716Hz -> 0 @ 1000000Hz
Oct 25 23:58:12.178: app-4696| HOSTINFO ((x * 2998529205) >> 33) + -10046224981836
Oct 25 23:58:13.968: app-4696| Vix: [4696 vixVIMProxy.c:3449]: VixVIMVmRequestTicketImpl: requesting old-MKS ticket for VM '[datacenter-2/shared1] CPXAV1100/CPXAV1100.vmx'
Oct 25 23:58:35.249: app-1704| Cannot connect to server myserver.com:902: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respondCnxAuthdConnect: Returning false because CnxAuthdConnectTCP failed
Oct 25 23:58:35.249: app-1704| CnxConnectAuthd: Returning false because CnxAuthdConnect failed
Oct 25 23:58:35.249: app-1704| Cnx_Connect: Returning false because CnxConnectAuthd failed
Oct 25 23:58:35.249: app-1704| Cnx_Connect: Error message: Failed to connect to myserver.com:902
Oct 25 23:58:35.249: app-1704| Vix: [1704 foundryVMPowerOps.c:5567]: Error VIX_E_HOST_TCP_SOCKET_ERROR in FoundryVMOpenSocketToVMXThroughAuthd(): unable to contact authd: 'Failed to connect to server myserver.com:902'
Oct 25 23:58:35.249: app-4696| Vix: [4696 foundryVMPowerOps.c:5046]: Error VIX_E_HOST_TCP_SOCKET_ERROR in FoundryVMFinishConnectingToVMX(): failing open because we can't contact authd
Oct 25 23:58:35.249: app-4696| VixVM_FinalRelease: Close VM socket.

vmware-vixWrapper:
Oct 25 23:58:12.108: app-2268| Log for VixWrapper pid=5804 version=1 build=build-368992 option=Release
Oct 25 23:58:12.108: app-2268| The process is 32-bit.
Oct 25 23:58:12.108: app-2268| Host codepage=windows-1252 encoding=windows-1252
Oct 25 23:58:12.108: app-2268| config points to non-existent implementation library 'C:\Program Files (x86)\VMware\VMware VIX\\ws_server_esx-4\32bit\vix.dll'
Oct 25 23:58:12.108: app-2268| config points to non-existent implementation library 'C:\Program Files (x86)\VMware\VMware VIX\\ws_server_esx-4\32bit\vix.dll'
Oct 25 23:58:12.108: app-2268| config points to non-existent implementation library 'C:\Program Files (x86)\VMware\VMware VIX\\ws_server_esx-4\32bit\vix.dll'
Oct 25 23:58:12.108: app-2268| config points to non-existent implementation library 'C:\Program Files (x86)\VMware\VMware VIX\\ws_server_esx-4\32bit\vix.dll'
Oct 25 23:58:12.111: app-2268| Loading Vix implementation library C:\Program Files (x86)\VMware\VMware VIX\\VSphere-4.1\32bit\vix.dll

I thought maybe it was because one of the ports was not open. But I checked both ports 443 and 902 and it looked like the ports are open:
C:\>C:\PortQryV2\PortQry.exe -n <myip> -e 443
Querying target system called:
<myip>
Attempting to resolve IP address to a name...
IP address resolved to <myip>
querying...
TCP port 443 (https service): LISTENING

C:\PortQryV2\PortQry.exe -n <myip> -e 902
Querying target system called:
<myip>
Attempting to resolve IP address to a name...
IP address resolved to <myip>
querying...
TCP port 902 (unknown service): LISTENING