The Japanese Wikipedia notes that before 1900, the kana sequence まいらせさうらふ (mairasesōrō) had its own kana ligature:
Poking around Wiktionary, my best guess would be that this is a set phrase in archaic keigo, but what exactly does this mean, and why was it apparently so common that it needed its own dedicated shorthand?
For comparison, almost all other ligatures were only two kana long and obviously common words (koto, yori, sama etc).
Yes, まいらせそうろう (in its most traditional spelling まゐらせさうらふ) was a high frequency humble marker in the once standard style for written communication called 候文【そうろうぶん】, which is based on the colloquial language in circa 12th century. Hiragana ligatures you see on your Wikipedia article represent common words and phrases utilized in the times 候文 and the cursive script (崩し字) were prevalent.
Under the style of 候文, そうろう (as such a humble marker) is bleached of its original meaning and only functions as the copula / main verb marker that symbolizes the style. まいらす, being the origin of today's polite marker ます, means from the most literal "offer" (= 差し上げる) to a general humble marker then to a simply politer marker (heavily used by women).
You can find some usage from the ligature's article, which reads:
一筆示し［まいらせ候］ = 一筆お示し（いたします／申し上げます）
I will (humbly) write you a letter
指のみ折り暮らし［まいらせ候］ = 指ばかり折って暮らしております
I am spending days only counting on my fingers
