Ironically, and maybe it's just me, but Liara's "lack of death" has caused me to care less about her because her plot-armor makes me know that, regardless of my actions or vested interest in her, she'll emerge just fine (at least until ME3). For all the other characters, that threat of death makes me more driven to care for their well-being and safety, and by extension I care for them as characters more than Liara.
Liara is still one of my favorite characters (all Bioware characters are great), but when you have a nigh-invulnerable, all-powerful information overlord who can't die no matter what you do and who routinely runs off to do her own thing without you, or a girl like Tali (or Jack or Ashley or anyone else) who realizes that they need your help and who willingly marches off into the hellfire on a self-appointed suicide mission where you know even one tiny mistake can end their life, I just feel much stronger emotions for those that could be lost.
I accidentally lost Mordin in a playthrough. I had no idea it was going to be HIM. I loved Mordin and his singing and his quirks. The loss of Mordin caused my following playthrough to ensure I definitely looked out for him, and I felt an attachment to him that far eclipsed that of Liara, who I knew was immune to the same sort of missteps from my decisions.
Basically, Bioware games, especially Mass Effect, thrive on actions and repercussions. Liara is the only one who is not only immune to death, but she's also relatively immune to your actions. No matter how you play the game, she will always do the same key things regardless of the way you treat her and follow the same path, no matter if you're male, female, renegade, paragon, love interest or not. She is rigid in a game that's fluid. You can influence small things about her (mainly if she's a love interest), but even Kelly is more easily impacted by your decisions and conversations.
It's not so much a criticism as an observation. It works for Liara to move the plot along, but at the expense of the attachment I feel towards other party members. For others, it could be different; a reassuring relief that their favorite character is immune from stupid leadership decisions and bad strategic suicide runs. Yet that's why she's so detached from me, or I'm so detached from her.
I'm much more interested in seeing how my decisions at Tali's trial concerning her father and the impact I've had with Legion and the Quarian/Geth war, as well as my intimacy with Tali on a personal level, will impact my friendship and relationship with her in the third game; where will she fall into place? As a leader of her people? As a vagabond without a home? As an embittered orphan? As a casualty of a foolish war I helped instigate? A girl matured by her experiences, or perhaps weakened by the immune system complications of our relationship? Can she die in ME3? How will her death in ME2 affect Shepard in ME3? Will the loss be significant? Will her appearance be highly beneficial?
All those variables aren't really applicable to Liara. Liara is unchanging, unmoving, and very consistent. No matter how you play the game, Liara survives both games, is essential to your resurrection, and ends up as the most powerful information broker in the galaxy by the end, no matter how much you screw everything else up. Her role must be the easiest to define and to write, but, for me, that makes her one of the least interesting because that story, her journey, rarely changes, unlike the sweeping and varied emotional character arcs of Jack, of Garrus, of Samara, of Thane, of Ashley, and many others, who can end up as entirely different people with entirely different fates depending on how you play the game.