The log timestamp should appear on each logical line. If the line wraps to multiple physical lines, the timestamp will only be on the first physical line. When I process log files, I generally assume that a line without a time shoud inherit the time from the previous line.
statement. You'll see that when it is reset in the script full timestamps appear on subsequent lines. When the script begins, it uses whatever timestamp the last script completed with. That becomes the document default. For a new document, I believe it starts the TimestampFormat from the windows system values.
Are you setting TimestampFormat elsewhere in the script?