Patricia Devlin lodged a complaint against the PSNI in 2020 for a failure to properly investigate a threat to rape her baby.
It was upheld by the Police Ombudsman and the case was reinvestigated.
On Monday the Public Prosecution Service (PPS) said that there was insufficient evidence to proceed.
Ms Devlin, who has written for the Sunday World and other publications, said it was a hugely disappointing decision.
"After I made the complaint to the Police Ombudsman, the PSNI then reinvestigated my original complaint and that individual was eventually questioned, the person they said (the PSNI) they tracked the message to.
"I was told I would have to wait for a decision from the PPS. That took almost a year and a half for a decision to be made.
"Now I have been told that there isn't enough evidence for a prosecution which is absolutely devastating.
"I feel again that I wasn't protected, that my son hasn't been protected."
Ms Devlin said that women in the public eye suffer more abuse than their male counterparts.
On Sunday, Alliance Party leader Naomi Long said Twitter needed to "up its game" when it comes to tackling online abuse, after she received "squalid and misogynistic messages".
"The levels of abuse that women are getting online is getting more vicious, more vile and It needs to stop," Ms Devlin said.
"My male colleagues aren't having their children threatened with rape, and nor should they.
"My male colleagues aren't having their appearance criticised, they're not receiving the same vile sexualised comments on Twitter and they're covering the same stories as I am, so gender has a huge part to play."
Ms Devlin said she was not sure she would make a complaint to the police if she was targeted again.
"The question is - is there any point in me making complaints to the police if I receive abuse again even on this scale? Because nothing seems to be done."
A spokesperson from the PPS confirmed it had received a file in January 2022 from the police in relation to the messages received, and had explored further lines of inquiry.
But, while it found the contents of the messages to be "grossly offence and menacing", the evidence to link the reported person to the message is insufficient.
"After careful consideration, and taking into account all the facts of the case, and the advice of independent counsel, it has been determined that for this reason the evidence was insufficient to provide a reasonable prospect of conviction of this individual for any offence," said.
The PPS said it is keen to meet with Ms Devlin if she wishes to discuss the decision and answer any questions.