-(ᄋᆞᆸ)사ᅌᅵ다 ＞ -(ᄋᆞᆸ)새이다 ＞ -ㅂ새다/ㅂ세다 ＞ -ᄇ시다 ＞ -읍시다
-읍시- + -오 → -읍시오
ᄉᆞᆸ (right afterwhen the stems end with ㄱ, ㅂ, ㅅ, ㅀ＊, or ㅎ＊)
ᅀᆞᆸ (right afterwhen the stems end with a vowel, or right after ㄴ, ㄹ＊, or ㅁ)
ᄌᆞᆸ (right afterwhen the stems end with ㄷ, ㄵ, ㅈ＊, or ㅊ＊)
＊ accompanied with consonant changes
According to 백문식 who wrote an etymology dictionary, those pre-endings (-ᄉᆞᆸ-, etc.) came from the verb 
다. meant 白 (to mention, to state, etc.).
-(ᄋᆞᆸ)사ᅌᅵ다 ＞ -(ᄋᆞᆸ)새이다 ＞ -ㅂ새다/ㅂ세다 ＞ -ᄇ시다 ＞ -읍시다
-읍시- + -오 → -읍시오
Nonetheless, it does not explain why -습시오 does not exist. Although 김현주's study covered various endings for 합쇼체 (= 하십시오체), it is still not so clear about where -읍시오 came fromᄉᆞᆸ시- existed before). At least we can say
김현주 claims that people who were not well-읍시오 is directly connected toversed in the court language used -ᄋᆞᆸ시- for the "addressee honorification" (notwhen the subject of a sentence was equal to the addressee. It seems that the author believes the following:
-ᄉᆞᆸ- + -으시- → -ᄋᆞᆸ시-
According to the dissertation, such an unordinary combination became possible when -ᄉᆞᆸ- became used for the "addressee honorification" because -으시- was (and is) used for 존경법 ("subject honorification"). If this is the case, the absence of -습시오 is quite understandable.
ᄉᆞᆸ (right after ㄱ, ㅂ, ㅅ, ㅀ＊, or ㅎ＊)
ᅀᆞᆸ (right after a vowel, or right after ㄴ, ㄹ＊, or ㅁ)
ᄌᆞᆸ (right after ㄷ, ㄵ, ㅈ＊, or ㅊ＊)
＊ accompanied with consonant changes
According to 백문식 who wrote an etymology dictionary, those pre-endings (-ᄉᆞᆸ-, etc.) came from the verb 다. meant 白 (to mention, to state, etc.).
-(ᄋᆞᆸ)사ᅌᅵ다 ＞ -(ᄋᆞᆸ)새이다 ＞ -ㅂ새다/ㅂ세다 ＞ -ᄇ시다
Nonetheless it does not explain why -습시오 does not exist. Although 김현주's study covered various endings for 합쇼체 (= 하십시오체), it is still not so clear about where -읍시오 came from. At least we can say that -읍시오 is directly connected to -ᄋᆞᆸ시- (not -ᄉᆞᆸ-).
ᄉᆞᆸ (when the stems end with ㄱ, ㅂ, ㅅ, ㅀ, or ㅎ)
ᅀᆞᆸ (when the stems end with a vowel, or ㄴ, ㄹ, or ㅁ)
ᄌᆞᆸ (when the stems end with ㄷ, ㄵ, ㅈ, or ㅊ)
According to 백문식 who wrote an etymology dictionary, those pre-endings (-ᄉᆞᆸ-, etc.) came from the verb 다. meant 白 (to mention, to state, etc.).
-(ᄋᆞᆸ)사ᅌᅵ다 ＞ -(ᄋᆞᆸ)새이다 ＞ -ㅂ새다/ㅂ세다 ＞ -ᄇ시다 ＞ -읍시다
-읍시- + -오 → -읍시오
Nonetheless, it does not explain why -습시오 does not exist (-ᄉᆞᆸ시- existed before).
김현주 claims that people who were not well-versed in the court language used -ᄋᆞᆸ시- for the "addressee honorification" when the subject of a sentence was equal to the addressee. It seems that the author believes the following:
-ᄉᆞᆸ- + -으시- → -ᄋᆞᆸ시-
According to the dissertation, such an unordinary combination became possible when -ᄉᆞᆸ- became used for the "addressee honorification" because -으시- was (and is) used for 존경법 ("subject honorification"). If this is the case, the absence of -습시오 is quite understandable.