The .xml logs are done by messenger itself, the .txt (or .ple for encrypted ones) logs are by Plus!. Based on a post by CookieRevised a little while back, this is probably caused by the .xml logs by Messenger, since they need to be adjusted each time message is saved (or something). If they are too long, it takes time, which is why they have some limit. The Plus! logs won't have this kind of problem - it just appends the new text to the end of the log.
You can turn off the logging by Messenger in > Tools > Options > Messages > Uncheck "Automatically keep a history of my conversations"
Try moving or renaming the log file for that contact, and see how it goes.
Edit: Cookie's posts I mentioned are in
Max Size Of Chat Log?!
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