First please put your code in CODE tags so it is laid out properly.

if ( $_ == "has gone down" ) { run start server command }
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Should be

if ( $_ eq "has gone down" ) { run start server command }
as it's a string comparison, but actually should be
if ( /has gone down/ ) { run start server command }
as it's a match you're looking for.
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You'll have to extract the timestamp from the matching line and save that to a file somewhere for comparison when you next run.