In cases like this, I generally use some kind of flag to prevent more than one instance from running at a time.

my $is_refreshing = 0;

$autorefresh_id = $root->repeat($rinterval*60000,\&refresh_func);

sub refresh_func {
    return if $is_refreshing;
    $is_refreshing = 1;

    ...
    #long running routine
    ...

    $is_refreshing = 0;
}
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You just need to make sure to reset the sentinal flag anywhere the routine can exit.