Note you can reapply after losing an appeal: the problem, as the quotes above noted, is that reapplying is likely to lead to a refusal again. So you are allowed to reapply, it is just not very likely to work, so they do not recommend it.
I do not think that particular website should have phrased it the way they did - "the sponsor may no longer sponsor his/her spouse ever again ...." It is not a rule or law that you cannot sponsor ever again. It is just that the doctrine of res judicata will apply. Res judicata means that "it is already decided." So if you reapply, using the same evidence, the result will be 'res judicata' - we have already decided this, so no visa.
But they did say "unless a new fact arises on the file ...", which means if there is new evidence, you may reapply and win. This new evidence has to be something that was not available at the time of the first application and appeal. Almost all of the time, more evidence of the same type you gave before will not be considered new evidence: so more phone bills, more proof of visits, more affidavits from family, etc., won't be enough. The cases I have seen win on appeal after a second sponsorship usually had these kinds of new evidence:
1. a child born after the first appeal, or
2. proof the couple has lived together for a significant amount of time after the first appeal (How long? A year was long enough for some; more than a year was not enough for another.)
In one case I saw, proof that the couple had continued their relationship after losing the first appeal was taken as enough new evidence that the relationship was genuine. Usually this is not enough new evidence, though.
here ..
