It's just pure luck! Hehe, just kidding.
Anyway, I recruited Tai Ho just as fine, I lost like 2 or 3 times before I beat him. Shilo, on the other hand, may be more difficult to deal with. At one time, I never lost to him, and at the other time, I lost to him so often that I have to reset the game.
I tried bringing low LUCK characters to recruit Shilo, and I lost to him often. When I brought high LUCK characters, I didn't lose as often. I'm only saying this based on my experience. So far, I haven't experienced any difficulty in recruiting Tai Ho, or I could just recruit Amada first as the ship captain. I had problems recruiting Shilo at times, though.
I think it's the average LUCK that determines winning in Chinchirorin since I can win that game easily even with just Riou in my party. Riou has a LUCK rank of A+, which explains why I'm so lucky in that game.
EDIT: Experiments on Shilo's Recruitment Game
I brought the following active party:
Riou (Lv 35, 122 LUCK)
Nanami (Lv 35, 99 LUCK)
Freed Y (Lv 27, 103 LUCK)
Gengen (Lv 33, 113 LUCK)
Chaco (Lv 29, 97 LUCK)
Clive (Lv 33, 49 LUCK)
Total LUCK: 583 (<600)
Average LUCK: 97
Lost most of the time, and even got a 1-2-3 one time, but got a 4-5-6 combination one time.
Shilo got triple 2's at one time.
Still, it's unknown whether the total LUCK or the average LUCK determines success in Chinchirorin when recruiting Shilo. The latter may be a factor once you have already recruited him, but I'm not sure if it's different when you ARE recruiting him.
That said, I'm still finding difficulties in recruiting Shilo. He's one pain in the arse to recruit.
Well, my suggestion is, if you're planning a speed run or if you want to recruit all the necessary SoDs in one batch, just place high LUCK characters in your party for the Two River sewers and then replace one of your party members with Chaco so that you can recruit Sid.
If you have recruited Sid already, replace Chaco or anyone in your party with Hix so that you can recruit him and Tengaar.
Odds are, this Two River party have already hit at least level 30 by the time you try to recruit Shilo. In addition, this saves you a lot of time having to replace your entire party with high LUCK, but low level characters.
I recommend this party:
(Note that they must have a LUCK rank of B+, i.e. at least 100 LUCK each by level 30+)
Hero (LUCK A+) - All-Around Healer (Bright Shield + Water/Earth)
Gengen (LUCK B+) - Attacker/Semi-Support (Earth)
Freed Y (LUCK A+) - Attacker/Semi-Support (Fire/Earth/Water)
*Nanami (LUCK B) - Spark Rune Bearer/Semi-Support (Earth/Water)
*Yoshino (LUCK B) - Supportive Magician (Earth/Water)
*Millie (LUCK A+) - Ranged Magician (Fire/Lightning)
**Shiro (LUCK B) - Spark Rune Bearer/Attacker
**Kinnison (LUCK B) - Supportive Magician (Earth)
**Luc (LUCK E) - Primary Magician (Blue Gate + Wind + Fire/Lightning)
* - You can place any character here in your FIRST Two River party. Replace them with Chaco and Hix (both LUCK B+) AFTER Two River. The number of * means that * is a different party than **.
A near-obvious choice would be Luc despite his abysmal LUCK stat due to his high magic affinity and access to level 4 spells such as Thor Shot, which is needed against the boss, Pest Rat.
Millie could have a higher Lightning affinity, but still can't have a level 4 MP slot at this point, unless you try Mt. Rakutei early, of course. Otherwise, you can still try multiple Bolt of Wraths with the other characters on the Pest Rat alright since most characters at this point now have a level 3 MP slot.
Another case is if you want to leave Nanami behind. Yes, you can leave her behind!
But one more thing. She can double as a support with a Water or Earth rune since she has an extra rune slot that most characters at this point don't. Also, she has a Unite Attack with Hero that deals major physical damage. So I don't think there's any reason to leave her behind. I mean, she may be weaker than the Hero, but is faster than him. But then, it's your choice.
Anyways, you can bring Freed's wife Yoshino in her place since their Unite Attack works just as fine. Then replace Millie with Shiro so you can still have a Spark Rune bearer, plus a nice Unite with Gengen, but without the Unbalance status.
Oh, you still don't like Yoshino? Try replacing her with Kinnison, instead. You'll have a nice Unite Attack with Shiro, again minus the Unbalance status.
It's not all about knowledge, but it helps.