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In the dictionary, 繰り返して is shown to have a special meaning "repeatedly". Of
course, the regular て form is the same. Which of the two is meant in
constructs such as

> われわれは数知れない失敗を繰り返してきた

> これを繰り返していけば…

For reference, here's how the 研究社 5th edition lists this word:

```

    くりかえす【繰り返す】 (kurikaesu)
    repeat; do over again; duplicate; 《文》 reiterate.
    おうむ返しに繰り返す　repeat 《sb's words》 like a parrot; echo [parrot] 《sb's words》
    ・繰り返して　repeatedly; over and over (again); again and again; time and (time) again
    ・繰り返して言う　say over (and over) again; repeat; 《文》 reiterate
    
```
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grammar て-form
Disambiguating 繰り返して: て form vs standalone word
繰り返して comes from 繰り返す. It is being used a lot in Japanese as you use the word
'repeat' a lot in English.

'~~~繰り返してきた' can be interpreted as "We have been repeatedly gone through ~~~."

<verb+て> words can never be put in dictionaries by itself. I've just searched
for some related Japanese texts in Google whether there are some exceptions,
but I couldn't find one. (Comments are welcomed if there are any exception for
them).

However, some phrases like ＜～て＋いく＞、＜～て＋くる＞ can be introduced as independent
expressions or idioms in Japanese.

Explaining the usage of '~てform' (て形 in Japanese) would need a small book to
cover all of them. (Imagine you are explaining someone the usage of 'which',
'that', 'who', 'where' in English)

So I recommend you to be just be familiar with the language itself first, then
study deeper more about the theoretical things.

However, you will be surprised someday that even Japanese don't know much
about the theories of Japanese by themselves. So please just to be familiar
with the language itself. Good luck!
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繰り返して is nothing but the て-form of 繰り返す. I find it a bit odd that it is listed
as if it is a standalone adverb in your dictionary. 繰り返し, with a ます-stem
ending, seems more qualified as one. In comparison, 繰り返して is clearly a verb
and, being transitive, sounds much more natural when it is used with a direct
object than otherwise.

Both your examples do have a direct object, as indicated with brackets below.

> われわれは［数知れない失敗を］繰り返してきた

> ［これを］繰り返していけば…

If 繰り返して were an adverb, the sentences would be grammatical without it, but
that doesn’t seem to be the case.

> x われわれは数知れない失敗をきた

> ? これをいけば…
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