You would have to show your code. Are you getting a message on the Serial monitor every time you plug it in that the RTC is not running? That should only happen the very first time you set up your RTC if the battery is installed.
Other than that, if you check for DST every time during startup, regardless of power loss, you will always keep subtracting off an hour. You can not just check the current RTC date- and then adjust it since you only want to do that adjustment 1 time. You could do something along the lines of storing DST flag in EEPROM and then when you detect a difference between the EERPOM and the RTC calculation, adjust the RTC and update your EEPROM flag.