Read your other posts after Oshallas hint. At the moment you step past incrementing the counter the next value is already read from $DATFILE. That is the culprit, not your '$cnt++'.
I just tested it with the perl debugger (perl -d) to be sure, and as expected, the while-test is not an extra step but just gets done behind the scene. So when you step over $cnt++;, the debugger really does $cnt++; while (<$DATFILE>) {. And if that file has a really long line, that might just be enough to send your script packing.
You might try this on your data to see if there is an overly long line in it:
while (<$DATFILE>) {
print $cnt,' ',length($_),"\n" if ($length>10_000);
$cnt++;
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