Unfortunately, what got Jenny fired was how she played it.
TA doesn't always reward "team-players", and I think that's what Jenny was. She was trying to help the others find the Leaver's Lace and stuff, and Vana just snubbed her. As she said on YF, she should've been more prominent, but she didn't really make any mistakes.
Unfortunately, that's what it all boils down to. On the show, it's really hard to strike a balance between being a team-player and a prominent character. If you're a team player, you'll be gone like Jenny. If a prominent character, you'll be loathed like Vana. Charleine is the only one ticking both those boxes at the minute - she's made a positive contribution to every task without overshadowing her team.
Gender also plays a role in this too. As GM said before, quietly confident male candidates tend to go further than abrasive ones, whilst it's the polar opposite with the women. Examples of this include the likes of Tom Pellereu, Solomon Akhtar and Tom Gearing, and Luisa Zissman, Debra Barr and Claire Young for the women. Steven from series 10 was loud and abrasive and fired quickly, whilst quiet Jemma went soon after.
Basically, if Jenny was male, she'd have gotten a lot further. That sounds much weirder than I'd envisioned...