OK, I'm pretty much out of "good" ideas.
Am I correct in assuming that - when WeatherLink is "frozen", it will not do anything locally (like bringing up the bulletin, or the browse window, or whatever)? With that assumption, is the timestamp on the 2014-01.wlk file consistent with the time that it froze? [And not changing].
Also, after it freezes and is restarted, can you quickly access the Browse Window and see what the most recent data is? Then (when you click "download" or whatever) observe how many records it is downloading. And finally, after the download, that it has all of the "missing" records from the past (no gaps)?
In other words, I'm about to agree that the problem is with the serial/USB adapter (hardware or driver). It would not hurt a bit to purchase a new adapter with accompanying CD of drivers for W7, and try that. (You could always return it to the store...).
Footnote: my XP system won't properly continue uploads to my site unless I turn the firewall completely off - but it does log the errors in the log file, and continue WU and CWOP uploads. So that's not like your problem.
HTH