In trying to determine why the first Sousaphone seems to dissappear shortly after it was built (sometime between 1894-96, by my estimation), here is one distinct possibility: Sousa was not a fan.
In the middle of the front page of Pepper's Musical Times and Band Journal from early 1896, where many of Sousa's band members praise their Pepper instruments, notice what Sousa himself says:
In case you can't read it, it says "All of the Pepper instruments in use in my Band are thoroughly satisfactory." I wouldn't exactly call that a ringing endorsement!
Could it be that the Pepper Sousaphone simply didn't live up to Sousa's standards of quality? It is curious that the first time we see a Sousaphone in the band (in my search of photos so far) is in 1898, and it turns out to be Conn's first model.
Of course, there may be more going on there, as well. In that very year, 1898, Conn outfitted Sousa's entire Band with his instruments - and Sousa raved about them from that point on. Pepper instruments, and the first Sousaphone in particular, quickly faded away.