If your reciprocal link checker doesn't work, first go to Admin Panel -> Settings -> System Configuration and be sure that you have the correct website URL listed, as this is what will be checked to ensure they're reciprocating (if no website URL is provided, the script installation URL is checked for instead).

If the reciprocal link checker unexpectedly doesn't check any links and just says 0 checked, it's likely that all articles are regular articles. Edit a article and change the type to reciprocal, then enter a reciprocal URL... after that, it should get checked.

If the dead link checker isn't working on some sites, those sites may be responding too slowly. Alternatively, there may be a connection problem causing your server to access them slowly.