with the log_file you have the option of saving it with a time_stamp or without one - in the latter case, it will be overwritten the next time your app runs.
There are, however, exact copies - which are not overwritten - on the server where your QV_Server is installed, probably in C/Program_Data/QlikTech/DistributionService/1/Log - there is a folder with a datestamp and in that there is one folder for every single reload of that day where you can still find your logs. - so I don't really see the point in having them all redundantly by activating the timestamping ...
Then you only have the challenge of somehow "remembering" when an error occured during reload.
There is a system_variable in QlikView, ErrorCount or so, that you can use to find out whether there was an error - with that you could build an IF_THEN block to generate some small txt file, you only need the timestamp there since with that you can always find the log you need in the logging_folders (set in the QMC).
P.S.: Oh - easier - you can see in the QMC the exact times when errors occured during reload - when you select a task (don't run it, just highlight) and click "Show task details" and activate the "History" tab. That log doesn't show you that much - but all you need is the time, then you can look in the log_folders.