Unless otherwise specified, TestComplete stores all logs for all test runs.
However, you can configure test complete to delete all but a certain number of recent logs. You can do this in TestExecute as well.
In TestComplete, go to Tools | Options | Engines and select the Logs option.
In TestExecute, run TestExecute stand-alone and right click on the systray Icon. Select Options and go to Engines and Logs.
There is a check flag in that section that reads "Store all logs". Make sure that is unchecked.
When that is unchecked, a different option is enabled that indicates the number of logs to store. If you set that to a number, after every test run, TestComplete will automatically delete any log entries in excess of that number, starting with the oldest.
For myself, on my test lab boxes that run automatically, I prefer to keep that value set to 50. That gives me at least a month and a half of history of the logs for reference (although I export my logs to a server location anyways) for immediate access. For my own personal machine where I'm doing development of tests, I set that down to something like 20 as I don't need a lot of history for all the debugging and development work I do on automation.
