To answer your question, imagine two situations.

Robin, a friend of yours, has told you that s/he will be competing in a chess competition.

In situation A, the competition has already taken place and you may or may not know the result.

In situation B, the competition has not yet taken place.

In situation A, imagining that Robin has lost, you would report:

Robin said (that) s/he wouldn't cry if s/he lost.

Imagining that you don't know the result, you might report:

Robin said (that) s/he wouldn't cry if s/he loses

or

Robin said (that) s/he wouldn't cry if s/he lost

The choice is just a matter of preference although I prefer the past tense. There are also other possible constructions such as: ...if she should lose.

In situation B, because the competition lies in the future, you can't know the outcome. Then you could say:

Robin says (that) s/he won't cry if she loses.

Or:

Robin said (that) s/he wouldn't cry if s/he loses.

Or:

Robin said (that) s/he wouldn't cry if s/he lost.

All three are acceptable and correct, depending on the context (with should lose as another option). If Robin has just spoken, you are more likely to report Robin says.... If she spoke some time ago, you would prefer Robin said....

In practice, native English speakers will frequently use a combination of both tenses regardless of which might be most appropriate.

The choice depends on the context, on timing and on your preference.

Let us put the problem sentences first :

• He said, "I will not cry if I lose."

• He said, "I wouldn't cry if I lost ( a game )."

The reporting speech i.e. the portion out side " ... " is kept in the past tense intentionally for a better understanding of conversion from direct speech to indirect. There would have been no change if the reporting speech had been in present or future tense.

The reported speeches in both the sentences are statements with a subordinate " if " clause. It could as well be any other subordinate clause with anyone of so many subordinating conjunctions. No matter.

" Will " has its past form " Would ". In the second sentence we make use of this " Would " as mentioned herein, not the modal " Would ", though " will " itself is a modal. We should not better go into those details.

What's within would change into corresponding past tense. So the indirect of the first sentence is :

★ He said that he would not cry if he lost.

As for the second we could not further distance " would " in the past. Let it be as it is. English tense system accommodates a developed form of SIMPLE in PERFECT. So we would change Simple past to Past perfect. Had it been in the Past perfect, we could not further distance it in time. Here we have the scope. Here's our second sentence :

★ He said that he would not cry if he had lost.