I want to provide an update about the status of our case.
I filed the I-134A for 3 of my beneficiaries (1 adult, 2 children) in mid 2022 and it was approved, and then they were approved for travel authorization by CBP. They stayed here about half a year and went back to Ukraine.
Fast forward to mid-2023, we tried to apply for them to come back here again after visiting family (there was a death of family member). I filed the I-134A for the same 3 beneficiaries, which was approved about a month later. We then sent a request for travel authorization to CBP. This request was rejected for all three beneficiaries. I suspect that the reason for the rejection is that you can only be paroled into the US under the U4U program once.
What I'm wondering is what the next steps are. I know that they were eligible to file the I131 for an Advance Parole document based on their 2 year U4U parole when they were inside of the US. However, are they still eligible to file for the I131 based on that 2 year Parole while in the Ukraine?