The 'F' flag after the destination (host.example.com.http:) is a FIN. So LWP appears to be sending a FIN in both cases.

At this point, to rule out any problem on your part, I would follow tye's suggestion. Setup your script(s) to do 1 iteration. Then cron (or windows schedule) them to run at your intervals.

Send me an email and I'll have you run this againnst my server. I can watch the ports from there.