If the number of sites is known, you could keep a file for all sites
and the related status (e.g. one line per site)

mysite.mydomain.org: ok
      could mean, last run the site could be accessed
mysite.mydomain.org: 2
      could mean, site not accesible for two consecutive tries

Therefore, compare your findings against the file, send an email if 1<=
errcount<=3, and update the file afterwards (incrementing or resetting
the error count)