The gemara quotes Rabbi Elazar no less than six(6) times saying, "שְׁלוּחֵי מִצְוָה אֵינָן נִיזּוֹקִין -- those on a mission to do a mitzvah are not harmed." (Pesachim 8a, 8b (twice), Qiddushin 39b, Chullin 142a (twice).)
There already exists a question on Mi Yodeya that takes this phenomenon for granted, and asks how far it goes. And at the time of this writing, there is only one answer there that begins, "From the ברייתא cited further in the Gemara, it would appear that any and all damages, even of the slightest and likeliest nature and occurring anywhere on one's property are included..."
But this is kind of hard to accept, since it is not that rare to hear stories of someone injured on their way to do a mitzvah.
The gemara does give one exception in one of the discussions of the quote (Pesachim 8b, translation and explanation from the Koren adaptation of R' Adin Steinzaltz):
וְהָאָמַר רַבִּי אֶלְעָזָר: שְׁלוּחֵי מִצְוָה אֵינָן נִיזּוֹקִין! הֵיכָא דִּשְׁכִיחַ הֶיזֵּיקָא שָׁאנֵי. שֶׁנֶּאֱמַר: ״וַיֹּאמֶר שְׁמוּאֵל אֵיךְ אֵלֵךְ וְשָׁמַע שָׁאוּל וַהֲרָגָנִי וַיֹּ֣אמֶר ה׳ עֶגְלַת בָּקָר תִּקַּח בְּיָדֶךָ [עֶגְלַ֤ת בָּקָר֙ תִּקַּ֣ח בְּיָדֶ֔ךָ וְאָ֣מַרְתָּ֔ לִזְבֹּ֥חַ לַֽה בָּֽאתִי׃]״.
But didn’t Rabbi Elazar say that those on the path to perform a mitzva are not [susceptible] to harm throughout [the process of performing the mitzva? The Gemara responds: In a place] where danger is commonplace it is different, [as one should not rely on a miracle,] as it is stated [with regard to God’s command to Samuel to anoint David as king in place of Saul:] “And Samuel said: How will I go, and Saul will hear and kill me; and God said: Take in your hand a calf [and say: I have come to offer a sacrifice to God” (I Samuel 16:2).]
There is a similar comment about "הֵיכָא דִּקְבִיעַ הֶיזֵּקָא, שָׁאנֵי -- . where danger is permanent, it is different" on Yoma 11a. Not sure why one says "דִּשְׁכִיחַ -- commonplace" while the other says "דִּקְבִיעַ -- permanent." Both use the same quote from Shemu'el I as their prooftext. (Thanks to @kouty in the comments for pointing out this source.)
But, I would add, we commonly hear stories of people who were harmed or lost large sums of money while doing a mitzvah in a situation we wouldn't consider dangerous or risky?
So, how do we intellectually honestly deal with this principle?