You're very close to the right answer, and if I take your code, it would look like this:

while (1) {
     next_time=time+60; 
     get_data_taking_55_seconds_give_or_take_a_few;
     sleep next_time-time;
     write_log_file;
}
[download]

Note that you will still have a +/- 1 second drift, so the exact time of measurements would still drift.

For higher accuracy, you pre-determine the times:

next_time=time;
while (1) {
     next_time=next_time+60; 
     get_data_taking_55_seconds_give_or_take_a_few;
     sleep next_time-time;
     write_log_file;
}
[download]