Everytime you power cycle the card you will need to perform the initialization sequence again.
Something like this
disk_initialize(0); // Re-initialize the SD card
pf_mount(&fs); // mount Fat FS
pf_open("logfile.txt"); // re-open file
pf_lseek(fs.fsize); // seek to end of file
pf_write(...); // Write block of data
Note that if the disk is re-initialized then you really should be performing pf_mount and pf_open again.
Also be aware of the limitations when using PetietFS for writing to files.
Cannot create file. Only existing file can be written.
Cannot expand file size.
Cannot update time stamp of the file.
Write operation can start/stop on the sector boundary.
Read-only attribute of the file cannot block write operation.
Particularly "Write operation can start/stop on the sector boundary." This requires that you write your data logs in multiples of 512 bytes.