I'm not sure at the moment if there's a built-in way to do this. But here is a stripped-down version of a script I've had in active use for about a year now to maintain a connection to an SSH server:

use warnings;
use strict;
use Net::OpenSSH;

my $connect_interval_s = 60;
my $command_interval_s = 60;

my $run=1;
local $SIG{INT}  = sub { $run=0 };
local $SIG{TERM} = sub { $run=0 };
OUTER: while ($run) {
    my $ssh;
    eval {
        $ssh = Net::OpenSSH->new( 'hostname', user => 'username',
                timeout => 10, kill_ssh_on_timeout => 1,
            ) or die "Failed to set up SSH";
        die "SSH failed to connect: ".$ssh->error if $ssh->error;
    ;1} or do {
        warn "Connect failed, will retry: $@";
        sleep $connect_interval_s if $run;
        redo OUTER;
    };
    # connection is up
    INNER: while ($run) {
        eval {
            my $rv = $ssh->capture('echo some command');
            die "Remote command failed: ".$ssh->error if $ssh->error;
            # ... do something with $rv here ...
        ;1} or do {
            warn "Command failed, will attempt to reconnect: $@";
            last INNER;
        };
        sleep $command_interval_s if $run;
    }
    sleep $connect_interval_s if $run;
}
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In addition, I've got this in my ~/.ssh/config for that hostname:

Host hostname
    User username
    IdentityFile ~/.ssh/filename
    ConnectTimeout 10
    ServerAliveInterval 10
    ServerAliveCountMax 3
    ExitOnForwardFailure yes
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