Maybe the game system and/or Star Trek is just not the right fit for that particular player.
It is not a fantasy setting like D&D or Warhammer where you accumulate XP and gain pretty significant advances really fast. That is totally OK for these types of games, but STA tries to emulate what is happening on the Star Trek TV shows.
And most of the time, characters don’t simply “advance”, they have minor or major character developments. And one unique thing about STA is that you have the opportunity to change your character, which is also something that is present in the TV shows but not really covered in any other system.
If you look at any character from the TV shows: Do they really “level up” a lot? The Doctor has some significant character development, but there are all tied to appropriate stories. Tom Paris was a medic before he got to Voyager, and I would say he sacrifices some of his roguishness (Command) to improve his medic skills (Medicine).
That all is the (unique?) nature of this system: You don’t “level-up” very fast or often, but you have the ability to change your character. And it perfectly fits Star Trek.
You can of course hand out Arc Milestones much more often, but that is not in the spirit of Star Trek. Also it might break the system if every Target Number is a 17 or something.