I am a BA Manager and have had in the past some BAs working offshore, in the office, from home and a mixture of the all three.
I disagree with the previous poster, that good jobs are not done via a job board. I advertise for any openings on job boards because I am told by our HR team that I have to. Even if I know personally a great candidate, or I actually know who I want to fill the role with - I still need to advertise it.
It is true that networking is a great way to get in with companies, but it shouldn't be seen as the only one.
Your problem about working for an International company is a little more tricky. I live and work in the UK, so can I ask, does it have to a US company, or would working for any company in the Western World do? E.g. A UK company (I'm not offering a job by the way!)
If it has to be a US company, can I ask where you are from? Sometimes, this causes problems with US companies, but it shouldn't. The only thing I would say is that working as a BA remotely can be tricky as you have to talk face to face with your stakeholders. This doesn't work well when you are remote. Just because a development team or the customer is not in that country, doesn't mean that the project team will also be abroad. Bear in mind that your 'Customer' is likely to be internal managers, who wont be abroad. How would you meet them if they want you to be face to face. As you say, some roles its fine to be located in a different country, sadly a BA isn't one of them really.
Having read your post I think you have two separate issues.
a. You want to work remotely for a US company
b. You aren't getting any replies to job applications
Bear in mind that a company will always prefer to have workers ON-SITE, whatever role they carry out. So the reality is that you will become down the pecking order because of that.
Next, you are (by the sounds of it) not a US national. This causes them extra headaches as often HR departments will veto anyone just on that basis. The US is, I believe, especially hot on this. I know here in the UK we care slightly less so. So again, you are even further down the order. If it is easier for them to employee someone who is a US national AND lives in the US, they will do so.
I would strongly suggest that these two reasons alone will be the answers to your problems.
So what can you do about them? Well, again, I would ask you "Is there a reason in particular that it has to be a US company?", secondly, do you have to work offshore?
If it does have to be a US company, and you do have to work offshore then you have only one real choice to be honest - look for a US company that has an office in your country. They will, depending on where you live, be few and far between. All of this means that you are limiting your options significantly. So I would strongly suggest that maybe you reconsider these options, and look to have a bit of leeway - could you work away from home, in the US for 6 months, for example?
Even then, I still don't think you will get many offers. Other countries than the US may be a better option, such as the UK or Germany?
I wish you luck though.