אֵין חָבוּשׁ מַתִּיר עַצְמוֹ מִבֵּית הָאֲסוּרִים - when one's own prayers are not enough

When Yishmael was cast into the wilderness and was close to death, the pasuk tells us that Hashem heard his cry and sent an angel to direct Hagar.  Rashi comments (21:17) את קול הנער – מכאן שתפילת החולה מתקבלת מתפילת אחרים עליו.  Meaning, even though the previous pasuk tells us that Hagar herself was weeping due to the distress her son was in, it was Yishmael's own prayers, his cries on his own behalf, not Hagar's, that Hashem responded to because a person's prayers on his own behalf are more efficacious than anyone else's.

Mizrachi asks: the gemara (Brachos 5b) tells us that when R' Yochanan was sick, R' Chanina came to visit him and helped him rise from his sick bed and get better.  

 רִבִּי יוֹחָנָן חֲלַשׁ. עָל לְגַבֵּיהּ רִבִּי חֲנִינָא, אֲמַר לֵיהּ: חֲבִיבִין עָלֶיךָ יִסּוּרִין? אֲמַר לֵיהּ: לֹא הֵן וְלֹא שְׂכָרָן. אֲמַר לֵיהּ: הַב לִי יְדָךְ! יְהַב לֵיהּ יְדֵיהּ וְאוֹקְמֵיהּ.

Asks the gemara: Why did R' Yochanan need R' Chanina's help to remove his illness?  Why could he not help himself?

אַמַּאי, לוֹקִים רַבִּי יוֹחָנָן לְנַפְשֵׁיהּ?

To which the gemara answers that a person who is ill cannot release himself from the bondage of his own illness -- help has to come from outside.

אָמְרִי: אֵין חָבוּשׁ מַתִּיר עַצְמוֹ מִבֵּית הָאֲסוּרִים

So how can it be that Yishmael's own tefilos could be more efficacious than the tefilos of his mother?  Aderaba, we see from the gemara that a person who is ill cannot get out of their situation without the help of an outsider!

Mizrachi answers that in reality, if a person can pray for themselves, that is more helpful than anyone else's prayers, but to do so requires the ability to concentrate.  R' Yochanan was so ill that he could not focus, and so he had to rely on R' Chanina's help.

Maharal in Gur Aryeh does not like the whole question. He explains that אֵין חָבוּשׁ מַתִּיר עַצְמוֹ מִבֵּית הָאֲסוּרִים does not apply to tefilah because even though it is the sick person himself who is doing the praying, it is Hashem, not the choleh himself, who cures the illness.  

 Maharal's approach is already alluded to in the Tur:  פירש״י מכאן שיפה תפלת החולה על עצמו מתפלת אחרים אע״פ דאין חבוש מתיר עצמו תפלה שאני כדאשכחן בחזקיהו ויסב חזקיהו פניו אל הקיר ויתפלל:

The difference between Maharal and Mizrachi may depend on how you understand how tefilah works here.  As we've discussed a few times (e.g. here, here and others), tefilah is not something supernatural, it's baked in the teva.  Hashem built nature in such a way that prayer has an effect on how it operates (see Maharal in Gur Aryeh on Braishis 2:5).  Maybe Mizrachi held that if that's the case, in the same way that the choleh can take medicine and be מַתִּיר עַצְמוֹ, so too his tefilah is מַתִּיר עַצְמוֹ .  It's not like Hashem is extending his hand and interfering with nature to pull him out of sickness,, which is how Maharal seems to view it.

Since we were talking about the whole idea of achvah last week, I wanted to mention the Chasam Sofer's answer. C.S. distinguishes between an aku"m and a yisrael.  When we are speaking about an aku"m (like Yishmael), there is no one who comes close to caring for the individual as much as the individual himself, and therefore, despite the limits of אֵין חָבוּשׁ מַתִּיר עַצְמוֹ מִבֵּית הָאֲסוּרִים, there is no one else whose tefilah can come close to being as effective as the choleh's own tefilah.  However, when we are speaking about a yisrael, the pain of one Jew is felt by all Jews, and therefore, the tefilah of someone else can be as sincere and meaningful as the choleh's own.  In that case, since  אֵין חָבוּשׁ מַתִּיר עַצְמוֹ מִבֵּית הָאֲסוּרִים , the outsider's tefilah can be more efficacious than the choleh's own (see Ksav Sofer who offers a different answer than his father's).