"You should not lose to her."

[federicourban]

Is the word order "neměla bys prohrát s ní" wrong? And why?

[igamenir]

Your word order is fine only when you want to strongly emphasize "s ní"="to her", e.g. "You may lose to most of the girls, they are quite good, but you should not lose to HER." In any other case, it would be too unnatural.