I agree with the others that there's no benefit to the higher ranked student to these take these challenge. Unless they add some details here the Challenged is incentivized to Ender's Game challengers, i.e. win the first battle so brutally that a second is never attempted. The battles starting only when the Challenged accepts and there being leeway on time to accept are good since it puts the time and place in their control. Gives them time to study their opponent instead of going in blind when the Challenger likely knows a lot about them. Also prevents them from being overwhelmed with challenges.
The 5 loss challenge limit is basically just set dressing since Luke is OP and will never lose unless he chooses to lose so if it gets applied it will be to some side character. If Luke was not OP then it would be a good addition since it would add stakes but it's meaningless here.
For reference, Luke's rankings are:
Overall rank: 2
Practical rank: 10
Studies rank: 5
Magic rank: 2
All shown ranks shown below, if they start revealing more ranks maybe I'll keep an updated list but I imagine it won't really expand by more than a handful of characters. I think it would've been better to list more people initially to flesh out the world building.
Overall ranking
1. Erina, First Princess
2. Luke, MC
Practical ranking
1. Ruby, Cat girl no information
10. Luke, MC
Studies ranking
1. Mirril, Commoner
5. Luke, MC
Magic ranking:
1. Libera, magic maniac, probable 3rd wife
2. Luke, MC