Do students needs to be specifically mentioned on grant proposals for projects funded by government agencies in the US? Let me start by giving some background.

I joined a research group about 3 years ago and at the time the PI (who became my advisor) told me that he would not be able to support me until either one of his PhD students graduated or he landed a new project from the agency that funds the research group. He told me that the wait wouldn't be too long because two students would graduate within the next six month (however he did say that it was not guaranteed) and I would be next in line to receive funding.

Well, it took those two students another two years to graduate. However, before they graduated the PI told me that their contract with the funding agency was being restructured and all current projects were being abandoned. He was proposing new projects instead of them however that meant that I was pushed back 3 or 4 places in the line to receive funding (which was based on seniority).

About a year later now, I am first in line again and the next project was suppose to be mine. However, my advisor just told me that they forgot to put my name on the project proposal and that although the project was approved I would not receive any funding. There are several staff members in our research group who are part of each project and he tells me that they are the only ones that were named on the proposal.

Does this sound plausible? I don't know much about how project proposals are structured and how funding is awarded. I'm getting a feeling that my advisor isn't being completely honest with me. I get the feeling that because I haven't complained much about funding to him in the past three years he is assuming that I can afford to go without it.   

I've actually had to hunt for a TA position every single quarter which would pay my tuition but provided a very small stipend (not enough to cover expenses).

P.S. these "projects" are separate from our thesis related research and are really just a means for supporting the students in our research group.
My experience is that students are not put in NSF proposals by name, but a slot is put in the narrative and budget with the name listed as TBD, "To Be Determined". It's possible that the PI failed to count all the heads correctly and was off by one. I would be surprised for this to happen in a small group, but if there were 10-12 students in the group, it could be easy to miss one.

Edited to add: It's worth noting that a particularly excellent student with lead or primary authorship on the papers that constitute the prior work for the grant might be highlighted in the grant text and budget, especially if the student has won some awards for the work