SD cards must be reinitialized if you remove power. If you remove an SD card while the file system is being updated you can cause a corrupt file system.
Newer SD cards buffer data in RAM so you must wait at least one second after the last SD access before removing power.
You should use a switch to tell the program you want to remove the card. When the program has closed the file and delayed for a second it can light an LED to tell you it is safe to remove the card.
Most SD sockets have a card detect switch. you could use the CD SW to detect when to initialize the card and reopen the file.
If you write a record about once a minute, the probability is low that you will corrupt the file system by just pulling the card since only a few ms is required to write the record. So if one in a few thousand are OK odds, just pull the card. You can connect the card detect switch to an interrupt.
I assume you flush data after every record.