Which of these is correct:
1-We are on a team that can't lose.
2-We are on a team that couldn't lose.

3-Last year, we were on a team that couldn't lose.

4-The year before that, we were on a team that can lose.

However, there is another, if less likely, possibility: 'We are on a team that couldn't lose (last year, but is much weaker this year).

Guest, Mister Micawber, Mask,

Whenever I see a question of the form seen here - essentially a multiple choice question - I usually judge it to be a "test question" which was encountered in an English course, usually with one right answer. I am not always correct in this :( , but usually.

In these cases, I restrict what I say to the essential concepts required to answer the question. Learners can easily be confused by too many complicated details about subtle possibilities not part of the original question.

I did not mean to imply that the oversimplified sequence-of-tense rule I gave was the whole story where this subject is concerned! I did, however, feel is was enough to answer the question posed.

As for
"This is a team that couldn't lose, even if they were one man short.",

I would say that there's nothing wrong with it. It has a typical

"IF past subjunctive, (THEN) conditional"
i.e., "IF ... WERE, ... WOULD ..."

tense structure within a relative clause modifying a noun in the main clause (in the present tense). The relative clause can be considered present in meaning (unreal condition and consequence in the present) even though not present in form.

Hope I've not muddied the waters even more!