thank you ... so you mean that "allows" always need an explicit object (me, you, the dog, Carl, them) ? In Italian there's a very similar construction where you can omit the object ( and in that case it makes reference to generic people/anybody )In general the answer is no, you don't have to repeat the "to".
However, your sentence doesn't seem quite right to me. The easiest way to put it right would be to put a pronoun in there:
Allows us to ...
Allows you to ...
If that is not a suitable fix for you then you need to re-write it a different way, but it does not work as you have written it.
The system allows for monitoring the targets and detecting possible threats."The system previously described allows to monitor the targets and (to) detect possible threats"
However, there should be no article "The" before "Method." The first sentence should read "Method X allows us to implement [something] ..."ok, so:
"The method X allows us to implement [sth]..."
"The method X allows implementing [sth]..."
I need to re-open this discussion since I've just found out that the form "allow for" actually means "to take into consideration" more than "to permit" .... So I wonder whether my previous sentence:I don't say that the others are incorrect, but I prefer this one by far.