In one video, someone calls out "sponsored by Gazprom" as officials take more than a minute to get the torch relit.
Elsewhere, a commenter on baltinfo.ru cites torches from the last Olympics that Russia hosted, the Summer Games in Moscow, saying, "They should have used the good Soviet ones from 1980."
The first flickering-out came at the gates of the Kremlin and seemed loaded with irony, given strident criticism ahead of these Olympics over human rights issues.
The second, third, and fourth occurrences, on the other hand, suggest that the torches are likely to burn out frequently over the next 65,000 kilometers of what's scheduled to be the longest Olympic torch relay in history.
They also might encourage spectators along the relay route to bring cigarette lighters -- just in case. Lighter manufacturer Zippo pokes fun at the Russian miscue on its Facebook page and through a #ZippoSavesOlympics Twitter hashtag.
The Krasnoyarsk factory that made the feather-shaped, red-and-silver torches for the Sochi Olympics is bound to face some tough questioning.
In the meantime, here's a Reuters video tour of that factory, including the detail that the facility also "produces ballistic rockets for submarines" and other rocket parts.
At one point in the video Viktor Filippov, who is identified as the factory's deputy chief engineer, says: "It's an overstatement to say it can keep the flame burning anywhere, but it can do that in the given temperature range."
Watch for yourself:
After the first incident, on October 6, Sochi Organizing Committee President Dmitry Chernyshenko appeared to stand by the manufacturer.
Chernyshenko insisted on Twitter that "the torches were tested in all possible ways and reliable burning will be guaranteed in any wind," according to baltinfo.ru. (The tweet appears to have since been removed, as it doesn't appear on his Russian-language Twitter feed.)
Since then, however, Chernyshenko has maintained Twitter silence on the topic.
-- RFE/RL Central Newsroom