From the Net::Telnet documentation:

Errors such as timing-out are handled according to the error mode action. The default action is to print an error message to standard error and have the program die.

Try adding the line:

$t->errmode("return");
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before the while loop. This should prevent the script from dying. See the entry for “errmode” in the “METHODS” section of Net::Telnet. (This also shows how to retrieve the error message when a command fails.)

Hope that helps,