She runs off in a huff at the end of Resurrection of the Daleks - the Doctor practically bundles Turlough into the TARDIS so they can leave before she changes her mind.
Tegan's character was one of the biggest surprises when I did my Big Rewatch a couple of years ago - I seem to recall liking her in 1981, but pretty much her only character trait was her ability to complain incessantly. Even after she leaves and returns, she's STILL whining all the time. And her costumes are awful (except that one in Enlightenment).
She looked stunning when she smiled, though - but Tegan never smiled if she could help it.
I was also surprised to find that I didn't like Jo Grant either, possibly as I knew the character from the books rather than the TV series and didn't have to put up with Katy Manning's excruciating wittle girl act.
I wasn't particularly surprised to learn that I still didn't like Adric, though...
Thinking about it, the only companion that actually works with the Fifth Doctor is Peri, who isn't around very long. Unfortunately, Peri doesn't work with the Sixth Doctor at all well, but then again, who would...?