I can't spot anything that could couse this problem (assuming the file permissions are right and your testing procedure was sound). I think you should just play with the code and try to write the program in some other way.

One way I would propose is to get rid of the exec call and instead pull the whole code from the server.cgi into the block where the exec is being called.

By the way there are race conditions in this code. Two (or more) instances of the program can read simultaneusly the "0" value from the pid file and think that they are the first. You should lock the file (see perldoc -f flock).