The Gemara on Amud Aleph discusses circumstances when a single witness is believed. Specifically this is in regard to testifying about the permissibility of a food or similar ritualry requirement.  

אֵימַר דְּאָמְרִינַן עֵד אֶחָד נֶאֱמָן בְּאִיסּוּרִין כְּגוֹן חֲתִיכָה סָפֵק שֶׁל חֵלֶב סָפֵק שֶׁל שׁוּמָּן דְּלָא אִיתַּחְזַק אִיסּוּרָא אֲבָל הָכָא אִיתַּחְזַק אִיסּוּרָא דְּאֵשֶׁת אִישׁ הָוֵי דָּבָר שֶׁבָּעֶרְוָה וְאֵין דָּבָר שֶׁבָּעֶרְוָה פָּחוֹת מִשְּׁנַיִם

One can say that we say that one witness is deemed credible with regard to prohibitions in a case such as where there is a piece of fat, and it is uncertain if it is forbidden fat and uncertain if it is permitted fat. In this situation, the piece can be permitted by a single witness, as there is no presumption that it is forbidden. However, here there is a presumption that this woman is forbidden as a married woman. If so, this is a matter of forbidden sexual relations, and there is no matter of testimony for forbidden sexual relations that can be attested to by fewer than two witnesses.

Rashi points out that even in a situation of presumption of a prohibited state, איתחזק איסורא , a single witness might still be believed so long as the single witness testifying has it in his power to effect the change that he is attesting to (it is known as בידו, literally “in his hands”.) Thus the person may testify the meat is kosher because he could have either bought kosher meat or slaughtered it himself.

Yismach Moshe (Ha’azinu) uses this understanding of presumption, chazakah and “what is in his hands” to explain a theologically difficult teaching regarding repentance. The Gemara (Yoma 85b) warns:

הָאוֹמֵר: אֶחֱטָא וְאָשׁוּב, אֶחֱטָא וְאָשׁוּב — אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה. 

With regard to one who says: I will sin and then I will repent, I will sin and I will repent, Heaven does not provide him the opportunity to repent, and he will remain a sinner all his days. 

Yismach Moshe wonders, is it really feasible to say that providence will not allow a person to repent if a person sinned, while rationalizing to himself that he will repent later? Unfortunately, many people stumble in this regard. If God or not to except this repentance, so many people would be left out in the cold. Others have attempted to answer this question by saying that the Gemara does not mean that God will reject their repentance, it just means that they will not be given extra divine assistance. However, Yismach Moshe finds that answer untenable. Based on the teachings of Gemara Succah (52b) even the righteous would not be able to resist temptation without God’s help. If so, surely those who already have sinned, and now need to repent, could not possibly achieve repentance if God were to hold back divine assistance. Therefore, we must interpret this teaching differently.

Ordinarily, if a person sins, but in his heart repents, he should be immediately forgiven and granted status of the righteous. True, he has a debt, so to speak, to follow up on his commitment, but it is indeed like a loan, and he gets goodwill credit immediately on the presumption that he will follow through with his word. However, if a person repeatedly sins or has in mind that he will sin and then repent, he has demonstrated that his intentions are not trustworthy, and his heart is corrupt. Therefore, his repentance will not yet be accepted by his resolve alone; he must follow up in action. In other words, he has a poor spiritual credit score.

Yismach Moshe cleverly compares this to the halakhos on our daf regarding the testimony of a single witness. When the situation is one of presumption of a prohibition, אתחזק איסורא he would not be believed, if not, for the fact that it is in his hands to still effect the change (בידו). But he only can rely on that argument if his trustworthiness has not been discredited. Unfortunately, the person who repeatedly sins, has degraded his standing and trustworthiness. He has shown, literally, “it is not in his hands“. Therefore, he cannot be granted forgiveness on the presumption that he will follow through. He must follow through on his resolve. And this is the meaning of the statement in Yoma: — אֵין מַסְפִּיקִין בְּיָדוֹ לַעֲשׂוֹת תְּשׁוּבָה. Heaven does not provide him the opportunity to repent as it is not in his hands.

A small point where I would argue a different position than the Yismach Moshe. He asked from the Gemara Succah that if the righteous need divine assistance in order to help them resist sin, surely a sinner must need divine assistance in order to repent. While there is strong logic to his point, that it would take more effort to repent and come back from a state of sinfulness than it takes to resist sin, one might argue differently. Once the person's desires are filled, he is no longer driven by the same lust and temptation. It actually may be easier to then repent, and require less divine assistance than to resist. Indeed, that very same Gemara makes a remarkable statement a half page earlier (52a):

כִּדְדָרֵשׁ רַבִּי יְהוּדָה: לֶעָתִיד לָבֹא, מְבִיאוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא לְיֵצֶר הָרָע, וְשׁוֹחֲטוֹ בִּפְנֵי הַצַּדִּיקִים וּבִפְנֵי הָרְשָׁעִים. צַדִּיקִים נִדְמֶה לָהֶם כְּהַר גָּבוֹהַּ, וּרְשָׁעִים נִדְמֶה לָהֶם כְּחוּט הַשַּׂעֲרָה. הַלָּלוּ בּוֹכִין וְהַלָּלוּ בּוֹכִין. צַדִּיקִים בּוֹכִין וְאוֹמְרִים: הֵיאַךְ יָכוֹלְנוּ לִכְבּוֹשׁ הַר גָּבוֹהַּ כָּזֶה! וּרְשָׁעִים בּוֹכִין וְאוֹמְרִים: הֵיאַךְ לֹא יָכוֹלְנוּ לִכְבּוֹשׁ אֶת חוּט הַשַּׂעֲרָה הַזֶּה! וְאַף הַקָּדוֹשׁ בָּרוּךְ הוּא תָּמֵהַּ עִמָּהֶם, שֶׁנֶּאֱמַר: ״כֹּה אָמַר ה׳ צְבָאוֹת כִּי יִפָּלֵא בְּעֵינֵי שְׁאֵרִית הָעָם הַזֶּה בַּיָּמִים הָהֵם גַּם בְּעֵינַי יִפָּלֵא״.

The Gemara answers: This can be understood as Rabbi Yehuda taught: In the future, at the end of days, God will bring the evil inclination and slaughter it in the presence of the righteous and in the presence of the wicked. For the righteous the evil inclination appears to them as a high mountain, and for the wicked it appears to them as a mere strand of hair. These weep and those weep. The righteous weep and say: How were we able to overcome so high a mountain? And the wicked weep and say: How were we unable to overcome this strand of hair? And even the Holy One, Blessed be He, will wonder with them, as it is stated with regard to the eulogy: “So says the Lord of hosts: If it be wondrous in the eyes of the remnant of this people in those days, it should also be wondrous in My eyes” (Zechariah 8:6).

What appears like a mountain to the righteous is barely a strand of hair to the wicked. Presumably, this is referring to the subjectivity of desire. When one’s desires are not met, it could lead to obsessing, and the desire could get stronger and stronger. However, the sinner does not feel the desire so strongly anymore after he sins. Then he cries tears of regret. So while his sincerity might in someway be suspect, the reality is that a sinner could have more regret, and come to it more easily, quite possibly, then the person in the throes of desire unfulfilled. This also may explain the teaching of Gemara (Yoma 29a): 

הִרְהוּרֵי עֲבֵירָה קָשׁוּ מֵעֲבֵירָה

Thoughts of transgression are worse than transgression itself.