As @Peter Cullen answer mention, your script will meet browser timeout first. So its good idea to provide some log output, then flush(), but connection have buffer and you'll not see anything unless much output provided. Here are code snippet what helps provide reliable log:
set_time_limit(0);
...
print "log message";
print "<!--"; print str_repeat (' ', 4000); print "-->"; flush();
print "log message";
print "<!--"; print str_repeat (' ', 4000); print "-->"; flush();