I do not know why Kepware client works. There are, however, some differences that are clear from the logs:

1) for some reason, you seem to be creating two connections at the same, and
2) (this is by design) QuickOPC creates an internal subscription (on each session) for checking the server status, besides the one subscription your code creates.

So, in total, if you count the effects of the two things above, there are 4 (2*2) subscriptions where it can be probably just one. That should still work, however. As to #2 (the status subscription), that can be turned off by a parameter in QuickOPC.

Changing timeouts etc. makes little sense. There is already enough "extra" time space to allow for normal variations in performance.

Regards

According to the log, the server has not sent a Publish response in time.

3002 0 4 01/08/2018 09:54:05 The OPC-UA subscription on client session with connect sequence number 1 to endpoint URL "opc.tcp://172.16.7.200:49320/" has been successfully created and checked, and given subscription ID 648. Revised publishing interval is 500, keep-alive count is 20 and lifetime count is 5000.
3021 0 2 01/08/2018 09:54:35 The OPC-UA subscription ID 648 publishing has stopped on the client session with connect sequence number 1 to endpoint URL "opc.tcp://172.16.7.200:49320/" for approximate current duration of 19953 milliseconds. The current keep-alive count is 20, the current publishing interval is 500 milliseconds, and the probationary period will be 5000 milliseconds. Further such errors on this session will not be logged.
3023 0 2 01/08/2018 09:54:40 The OPC-UA subscription ID 648 publishing has halted on the client session with connect sequence number 1 to endpoint URL "opc.tcp://172.16.7.200:49320/" for approximate current duration of 24965 milliseconds. The current keep-alive count is 20, the current publishing interval is 500 milliseconds, and the probationary period was 5000 milliseconds. Further such errors on this session will not be logged.

Regards