Here is a hypothetical. It is the days of Shlomo Hamelech. There are a group of people who are in fact neviei sheker who arise and start prophesying doom and gloom. They stress teshuva and increased mitzvah performance, but not necessarily those things which optimally need improvement, or even need any correcting, since they are not actually privy to the desires of the One On High. And they echo one another, and promote a message more-or-less consistent with one another. Why do they do this? Who knows. Maybe some are lunatics. Others see it as a necessary way to increase the spiritual level of klal Yisrael. Maybe others are misguided and they viewed their own thoughts in their dreams as prophetic.
What are the obligations of the average intelligent Israelite vis a vis these false prophets? Must he heed them because they claim to be nevi'ei Hashem? Because they have long beards, or the title "rabbi". (Yes, I know this detail is anachronistic.) What is they have a strong army of gullible followers who were influenced to teshuva because of these prophecies. Must one believe then, and become a follower as well?
These false prophets are either careful or lucky. Despite making repeated false predictions, they claim that teshuva prevented this disaster or that from actually occurring, but the next tragedy is just around the corner. The claims are unfalsifiable, because of the flip-side claim that teshuva averted the decree; and because indeed halachically since it is a prophecy of woe, indeed Hashem might well cancel the decree because of repentance or prayer, as in the case of the navi emes, Yonah. If their claims are unfalsifiable, how long may these nevi'ei Sheker hold klal Yisrael hostage to their particular vision of Judaism?
It is to deal with precisely this sort of situation that the Torah sets up tests before believing a navi, even one preaching a message of doing mitzvos and/or teshuva. To cite the Mishneh Torah, hilchos yesodei haTorah, perek 10:
That is, despite him saying positive messages, one doesn't need to believe him to be a navi emes even though people say that he is a tzadik, and a holy mystic, and even though he has many followers, or the title rabbi, or a long white beard. Rather, you test him. He need not perform miracles as signs. Rather, he needs to predict the future. And you may test him in this manner multiple times, I suppose to ensure that it is not just coincidence. So he predicts, and you wait. If he repeatedly succeeds, then he is established as a true prophet. Otherwise, as a false prophet. Even if you can kvetch the prediction to be true, because that could well be coincidence. Every last detail needs to be accurate. So, to give a hypothetical example, a mere skirmish a day later than a predicted apocalyptic war wouldn't count as an accurate prediction.
א כָּל נָבִיא שֶׁיַּעֲמֹד לָנוּ וְיֹאמַר שֶׁה' שְׁלָחוֹ, אֵינוּ צָרִיךְ לַעֲשׂוֹת אוֹת כְּאֶחָד מֵאוֹתוֹת מֹשֶׁה רַבֵּנוּ אוֹ כְּאוֹתוֹת אֵלִיָּהוּ וֶאֱלִישָׁע, שֶׁיֵּשׁ בָּהֶן שִׁנּוּי מִנְהָגוֹ שֶׁלָּעוֹלָם; אֵלָא הָאוֹת שֶׁלּוֹ שֶׁיֹּאמַר דְּבָרִים הָעֲתִידִין לִהְיוֹת בָּעוֹלָם, וְיֵאָמְנוּ דְּבָרָיו, שֶׁנֶּאֱמָר "וְכִי תֹאמַר, בִּלְבָבֶךָ: אֵיכָה נֵדַע אֶת-הַדָּבָר . . ." (דברים יח,כא).ש
ב לְפִיכָּךְ כְּשֶׁיָּבוֹא אָדָם הָרָאוּי לַנְּבוּאָה בְּמַלְאֲכוּת ה', וְלֹא יָבוֹא לְהוֹסִיף וְלֹא לִגְרֹעַ, אֵלָא לַעֲבֹד אֶת ה' בְּמִצְווֹת הַתּוֹרָה--אֵין אוֹמְרִין לוֹ קְרַע לָנוּ אֶת הַיָּם אוֹ הַחֲיֵה מֵת וְכַיּוֹצֶא בְּאֵלּוּ, וְאַחַר כָּךְ נַאֲמִין בָּךְ. אֵלָא אוֹמְרִין לוֹ, אִם נָבִיא אַתָּה, אֱמֹר לָנוּ דְּבָרִים הָעֲתִידִין לִהְיוֹת; וְהוּא אוֹמֵר, וְאָנוּ מְחַכִּים לוֹ לִרְאוֹת הֲיָבוֹאוּ דְּבָרָיו: אִם לֹא יָבוֹאוּ, וְאַפִלּוּ נָפַל דָּבָר אֶחָד קָטָן--בַּיָּדוּעַ שְׁהוּא נְבִיא שֶׁקֶר.ש
ג וְאִם בָּאוּ דְּבָרָיו כֻּלָּם, יִהְיֶה בְּעֵינֵינוּ נֶאֱמָן. [ב] וּבוֹדְקִין אוֹתוֹ פְּעָמִים הַרְבֵּה. אִם נִמְצְאוּ דְּבָרָיו כֻּלָּם נֶאֱמָנִין, הֲרֵי זֶה נְבִיא אֱמֶת, כְּמוֹ שֶׁנֶּאֱמָר בִּשְׁמוּאֵל, "וַיֵּדַע, כָּל-יִשְׂרָאֵל, מִדָּן, וְעַד-בְּאֵר שָׁבַע: כִּי נֶאֱמָן שְׁמוּאֵל, לְנָבִיא לַה'" (שמואל א ג,כ)ש.שש
The Rambam says later in the perek that negative predictions which fail to occur do not establish him as a false prophet:
ח [ד] דִּבְרֵי הַפֻּרְעָנוּת שֶׁהַנָּבִיא אוֹמֵר, כְּגוֹן שֶׁיֹּאמַר פְּלוֹנִי יָמוּת אוֹ שָׁנָה פְּלוֹנִית שְׁנַת רָעָב אוֹ מִלְחָמָה וְכַיּוֹצֶא בִּדְבָרִים אֵלּוּ--אִם לֹא עָמְדוּ דְּבָרָיו, אֵין בְּזֶה הַכְחָשָׁה לִנְבוּאָתוֹ; וְאֵין אוֹמְרִין הִנֵּה דָּבָר דִּבַּרְתָּ וְלֹא בָא: שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא "אֶרֶךְ אַפַּיִם וְרַב-חֶסֶד, וְנִחָם עַל-הָרָעָה" (יואל ב,יג; יונה ד,ב); וְאִפְשָׁר שֶׁעָשׂוּ תְּשׁוּבָה וְנִסְלָח לָהֶם כְּאַנְשֵׁי נִינְוֵה, אוֹ שֶׁתָּלָה לָהֶם כְּחִזְקִיָּה.
This is so. However, while they do not establish him as definitively a false prophet (such that the claim was not really falsifiable), neither do they qualify him as a true prophet. Rather, this is an unfalsifiable claim. He is not really going out on a limb. I suppose that with multiple negative predictions which come true, he would indeed still be considered a true prophet -- say, if his rate of prediction was very high.
And if he, and those of his fellowship, do not first establish themselves as true prophets, with multiple accurate predictions; and if he, and those of his fellowship also make numerous negative predictions which fail to pass, then it may be so that we cannot establish him as a navi Sheker. We can, however, point out that he has not yet established himself as true, and also point out his (and their) extremely low batting average. This would seem a fair and relevant point. Not only did we have no reason to believe him in the first place, but he keeps striking out on these technically unfalsifiable claims! Surely we are allowed to consider this when deciding whether to grant him the benefit of the doubt as a true navi, as a matter of reshus.
Leave off the hypothetical, and consider the present day. We have autistics; we have leaders of Baal Teshuva movements; we have kabbalists, all making claims of doom and gloom. They are not technically neviim, such that they would be subject to the rules of establishing them as a navi sheker or navi emes. But they claim knowledge of what is going on On High. Are people obligated to believe them, because they have long beards, because people call them kabbalists and mystics, because they have armies of (possibly) gullible followers, or because they have the title 'rabbi'?
I don't see it. Rather, what I see is a parallel situation to the one of navi sheker. Random mystics or (in some cases) lunatics cannot hold klal Yisrael hostage and dictate that there are goings-on On High, in a way that all Jewry must listen to them. And they cannot simply make repeated warnings, over more than a decade, of impending doom, which fails over and over again to materialize. First establish yourself as authentic, by making multiple true predictions. Once they have this chazaka, we need to listen to them. Until that point, suspicion is allowed, and (IMHO) repeated failure of predictions, of the unfalsifiable variety, can legitimately increase one's suspicion about their authenticity.
Also, since the hamon am does not realize this, that there is no obligation to believe these repeated unfalsifiable negative claims, it is fair game to point out the failures of prediction, and keep track of the batting average. Especially since eventually, with enough negative claims, something is going to randomly hit close to the mark, as in the case of the Tsunami kabbalist, who made at least nine false predictions for the one he got right, and even the one he got right was not specific and even then not really on the mark.