I've sometimes thought about what constitutes a "continuous run" as it applies to game shows, and the rule I use for myself is that a show "resets" after 12 months or so of no new episodes.
So that means "Concentration" had a continuous run from 1958-78, in spite of changing production companies (which it actually did twice, come to think of it -- B&E to NBC in '58, NBC to G-T in '73). Likewise, "Truth or Consequences" from 1954-65 and "Pyramid" from 1973-81 would count as continuous runs in my book, since there was never a 12-month gap between new episodes.
The syndicated revivals of WML?, TTTT, et al. in the 1960s count as new runs because they went a year without new shows. Of course that leaves us with really borderline cases like "Battlestars", with 49 weeks separating the first and second versions, but that one isn't likely to make any longest-running lists!
(I also recognize that the syndicated "Truth or Consequences" debuted about 51 weeks after the network run ended, but I tend to count it as a separate run, given how close it is and the fact that not all markets necessarily starting running it on the same day.)