Буду очень благодарен, если ответите поскорее. Мой заказчик ждет.
Finally the issue has been resolved in a manner that has nothing to do with the plugin.
Another facts to consider are that the site have a small traffic and is located on the cheap hosting. So every process matters.
The host support replied that the limit is set for all user processes, not only PHP, and the calling of mail() creates additional process.
Well, I don’t clearly understand how this limit can cause this particular issue. Does calling of mail() function actually create additional PHP process? I’ll better write to my host again.