I am wondering, also, what country you were doing all of this in? Do you know if they have labs there that do paternity testing certified by the family court for determining paternity legally? You might contact the court system in the country where he lives for a list of labs they consider valid for this purpose.
As far as the past test is concerned, don't waste a lot of time worrying about whether the lab did or did not do things correctly, just assume the situation was suspect and go forward with a new test now, using authority.
By the way, I'm assuming you know the man is the father. If you just think he is, and there is another possible candidate, you REALLY want the testing to be reliable. (If the latter situation, you could test with the other candidate; he might be easier to deal with than the guy who is skipping out on all the tests.)
Anyway, if this particular man who has skipped out on all the tests is a prize worth chasing, such as, there is financial support you could gain for your child, or some positive name recognition that you feel would benefit your child in the future, you should definitely be seeing a lawyer in that country. Failing the ability to do that, go to the embassy here and talk to them about your problem and see what they recommend. Talk to lab and the guy's family, someone else might be able to do a DNA test in his place. If the guy has some local fame, you could even go to the press in his country. But I wouldn't take any of those steps until you are sure he has to be the dad, by ruling out all other possibilities, and also I wouldn't make that kind of fuss if the guy is just some garden-variety irresponsible creep who does not have any money or any interest in the child either.
It does not sound like you can trust the situation; knowing the guy had dodged tests before, I would have insisted the whole thing be done with lawyers present and you witnessing him doing the swab and your child's swab and being there when both were taken into custody at the neutral lab or put into the post, in other words, every step should be done with neutral witnesses whose job it is to be sure there is no substitution of the swabs or of the package with the swabs in it. There are a hundred ways someone who does not want to be named a father can switch samples around.
If this guy is just some jerk, I am not sure that all your trouble to establish him as the father is worth it, since it does not sound like he is going to be an interested father even if the test comes up positive. But if you think there is a good reason to do it (for example, if you could get child support for your child) I can see doing it. But stop doing it in such a casual way. Leaving swabs to be mailed off later is ridiculous, anyone's swab could have been sent in.
I should also add that the USA lab also commented that the lab hadn't followed standard for number of markers tested