Write an program that terminates after 60 seconds - Cops' Thread
Perl 52 bytes (26 edits allowed) (Safe, technically speaking)

sub a{[gmtime+time]-&gt;[0]^$x}$x=a;0 until a;0 while a

Unfortunately, I don't think it's possible to write an uncrackable Perl program (it should become obvious why if and when this is cracked; being able to edit half the program is just too much), but this algorithm should be very hard to change to wait for any length of time other than 1 minute.
Marking this as safe, as nobody's officially submitted a crack for 14 days (although someone unofficially cracked it by just writing a separate program and commenting out the existing code). The basic idea of the program is as follows: we look at the seconds digit of the time, loop until it changes, then loop until it returns to its original value. This requires quite some changes to alter to a length of time other than 1 minute, 1 hour, or 1 day (although 26 edits is easily enough – you can do some modular arithmetic on the seconds value to determine a new target to wait until – but nobody found that solution).