It's just a matter of luck. Sometimes it takes forever and sometimes it's quick and painless. If you don't get it, you won't have the complete badge set that you can give to someone later in the game in exchange for some items. The thing is, the items you get aren't really anything special. Every time I've played this game, I got all the badges and got the items, but I never used them.
"That was pretty interesting! But dropping a war ship on me is cheating! Take it back!"-Id from Xenogears
Tell me about it. That's why I keep a save with that dude already defeated, in case I wanna play the game again (which I inevitably do, once a year, no matter what). I watch the opening for the hell of it and then load up the save.
He's not exactly an evil tactical genius, though. I've noticed that very often he just alternates between throwing what would have beaten you in the last throw and throwing exactly what you threw. It's of course not 100%, but try it and you may get lucky.
In my opinion, this is for completionists only. The two items you receive for collecting all three badges can be bought for fairly cheap prices a small time later in the game. There are multiple times you have the option to 'waste time' for items in Xenogears, and pretty much every other example is time better spent than on that stupid badge.
Consider that, as long as you win more than you lose, you're still turning a profit. If you get 4 in a row, then lose, yes, it's frustrating that you have to start from scratch, but you made a net gain of 150 G.
It takes the edge off of losing, looked at that way.
"As the good archmage often admonishes me, I ought not to let my mind wander, as it's too small to go off by itself." -Danilo Thann