Hmm...even Generate Logfile is unchecked. The only other location I'm aware of that has anything to do with generating log files is in the User Preferences on the Design tab. It, however, does not have a box for timestamps. How you're even generating log files is odd.
What version are you using? (my current version at home is 11.2 sr4, work is 11.2 SR6)
Those are Server logs. The relevant setting is on the QMC System, Qlikview Servers, Logging tab. In the "Split Files" section, something other than "Never" is selected. If you don't want them split by date, or want them split on a less frequent interval, change the setting there.