Played 3 games now, and every time I play I get through the initial melee, and then get the "sorry, you don't have the killer..." message. Went through source, and it appears that it will happen every time. If the below is accurate, it looks like as long as you are 'rookie', you won't get a battle.

From BattleArena.xml:
(not arenaRank)
(scrShowPane gScreen "FirstFight")

(= arenaRank 'rookie)
(scrShowPane gScreen "NoMoreMelees")

(= arenaRank 'gladiator)

nms 6 Aug 2019:

Are you sure you got enough kills? Was the 50 credit per kill payment working?

balentius 6 Aug 2019:

Previously, I was able to fight twice to move past the melee battles. Having said that, I think I was paid, but I'm not certain. It definitely counted my kills; I don't remember if I was awarded credits or not.

george moromisato 4 Nov 2019:

Need to investigate.

george moromisato 11 days ago:

I think this is working properly. You must kill at least 20 ships in 5 melee rounds. If you don't, then you get the NoMoreMelees message.