Thank you for the response KateG . We did do several tests and feel relatively confident the issue was the Windows machine that I was remotely connecting to (I think that would make it the host). I was able to successfully able to connect to a different machine in our office so it did not seem to be an issue with my Mac or the the Logmein app.
After that we tried to focus on the network card driver. Yesterday I uninstalled the network card and then restarted the windows machine (to reload the driver). This seems to have fixed the problem for today. Will keep an eye on it as I continue to use the original setup.
