Objection 1. It would seem that sinners impetrate nothing from God by their prayers. It is written (John 9:31): "We know that God doth not hear sinners"; and this agrees with the saying of Proverbs 28:9, "He that turneth away his ears from hearing the law, his prayer shall be an abomination." Now an abominable prayer impetrates nothing from God. Therefore sinners impetrate nothing from God.
Objection 2. Further, the just impetrate from God what they merit, as stated above (15, ad 2). But sinners cannot merit anything since they lack grace and charity which is the "power of godliness," according to a gloss on 2 Timothy 3:5, "Having an appearance indeed of godliness, but denying the power thereof." and so their prayer is impious, and yet piety it required in order that prayer may be impetrative, as stated above (15, ad 2). Therefore sinners impetrate nothing by their prayers.
Objection 3. Further, Chrysostom says: "The Father is unwilling to hear the prayer which the Son has not inspired." Now in the prayer inspired by Christ we say: "Forgive us our trespasses as we forgive them that trespass against us": and sinners do not fulfil this. Therefore either they lie in saying this, and so are unworthy to be heard, or, if they do not say it, they are not heard, because they do not observe the form of prayer instituted by Christ.
On the contrary, Augustine says (Tract. xliv, super Joan.): "If God were not to hear sinners, the publican would have vainly said: Lord, be merciful to me a sinner"; and Chrysostom [Hom. xviii of the same Opus Imperfectum] says: "Everyone that asketh shall receive, that is to say whether he be righteous or sinful."
I answer that, In the sinner, two things are to be considered: his nature which God loves, and the sin which He hates. Accordingly when a sinner prays for something as sinner, i.e. in accordance with a sinful desire, God hears him not through mercy but sometimes through vengeance when He allows the sinner to fall yet deeper into sin. For "God refuses in mercy what He grants in anger," as Augustine declares (Tract. lxxiii in Joan.). On the other hand God hears the sinner's prayer if it proceed from a good natural desire, not out of justice, because the sinner does not merit to be heard, but out of pure mercy [Cf. 15, ad 1], provided however he fulfil the four conditions given above, namely, that he beseech for himself things necessary for salvation, piously and perseveringly.
Reply to Objection 1. As Augustine states (Tract. xliv super Joan.), these words were spoken by the blind man before being anointed, i.e. perfectly enlightened, and consequently lack authority. And yet there is truth in the saying if it refers to a sinner as such, in which sense also the sinner's prayer is said to be an abomination.
Reply to Objection 2. There can be no godliness in the sinner's prayer as though his prayer were quickened by a habit of virtue: and yet his prayer may be godly in so far as he asks for something pertaining to godliness. Even so a man who has not the habit of justice is able to will something just, as stated above (Question 59, Article 2). And though his prayer is not meritorious, it can be impetrative, because merit depends on justice, whereas impetration rests on grace.
Reply to Objection 3. As stated above (07, ad 1) the Lord's Prayer is pronounced in the common person of the whole Church: and so if anyone say the Lord's Prayer while unwilling to forgive his neighbor's trespasses, he lies not, although his words do not apply to him personally: for they are true as referred to the person of the Church, from which he is excluded by merit, and consequently he is deprived of the fruit of his prayer. Sometimes, however, a sinner is prepared to forgive those who have trespassed against him, wherefore his prayers are heard, according to Sirach 28:2, "Forgive thy neighbor if he hath hurt thee, and then shall thy sins be forgiven to thee when thou prayest."
Source: Summa Theologica (New Advent)