This happens to me all the time, only people don't give up on the files, I've shut my computer off for over 4 hours, and when I turn it back on again, I get those messages again.
The best things I have found to do is to either:
1.) Stay connected all the time, not always an option though.
2.) Disconnect from the network around 20 minutes before you plan to be done with it, after you are done searching, but before you have finished downloading files. This should give people time to finish some of the files, and will cut you off from further searches.

That said, the pings are completely harmless, so aside from being a slight annoyance, you don't have much to worry about.