No evidence. The showrunner claims to have killed off Andrea for creative reasons.
I can't find any evidence that any of the creative staff or producers were unhappy with Holden's performance.
In a June 2013 interview by Hollywood Reporter with Glen Mazzara, the showrunner during Holden's exit, he claimed that killing off Andrea was done to show that "no one is safe" and to motivate certain actions by Rick:
Looking at season three as a whole, you've killed off a few major characters — including one who's still alive and kicking in the comics. What was the decision like to kill Andrea?
MAZZARA: They're all difficult decisions. I thought it was important that we always show that no one is safe. It's also important to show the effect that these deaths have on our other characters. Andrea's death, for example, I knew Rick was going to finally open up the gates of the prison after a season in which he's trying to hide away from the world and lock everybody away and keep them safe. He realizes what that means -- that our group is now becoming isolated and will be picked off, that his own son is on the road to becoming the Governor (David Morrissey), so he has to open up the gates and let other people in and be compassionate. At the end of the finale, he brings in these women, children and elderly people and the group is going to transform. There needed to be a blood sacrifice for that, and there had to be a price that was paid. Andrea paying that price was important. She is unable to re-enter the group. In a way, a lot of what she did was bring the two groups together. But she's never able to enter the prison and be reunited in a full way with Rick's group. That was an ultimate sacrifice that was worthy of the season finale.
When did you know Andrea would pay the ultimate price?
MAZZARA: It developed throughout the season. I always knew that Rick opening the gates and letting people in was always a plan. The idea of Andrea's death emerged halfway through the season.
Laurie Holden suggests the character was written in such a way as to be different from Andrea in the comics.
Later that year, at Fan Expo Canada, Holden suggested that Andrea in the show was written to be different from Andrea in the comics (rather than the difference being a result of her acting). She expressed regret that her character was not written to be more like the one in the comic book:
"Your character is fairly close [to the comics]," Laurie said to Steven [Glenn]. "I wish I could have been a writer on the show because it would have been very different. The Governor would be dead by now. [The] writers have creative license and they do things to keep it interesting. I loved every moment working on that show, I loved the character of Andrea. I wish that I had been like in the comics and been able to end up with Rick in the end and to have been that killer sharpshooter. But I don't write the stuff and it was someone’s decision to go that direction and you just do the best job you can. It's just a different medium. You just embrace what they write."
To my knowledge, these statements by Holden have not been countered by anyone working on the show.