Can I recruit entei and the other legendarier after the SECOND time I defeated..

Yes you can recruit him only if you have their friend area..Which the name I forgot.

You can only recruit him the second time. You may not, I had to defeat him five times to recruit him.

OK, once again, I don't know why NO ONE ever mentions that you usually cannot recruit on the first encounter, then possibly on the second one IF you have their friend areas bought AND your Leader's level is HIGHER than the level of the Pokemon you are trying to recruit!! Plus you need to have room in your party, too! You might only not be a high enough level, and it's going to most likely take multiple tries to recruit ANY legendary-it's just not that easy, sorry, that's the nature of the game. If you want, just level your leader up to Level 90 or above, get a friend bow, buy all the friend areas, then go recruiting-that's the best possible position you can be in is above level 90 with a friend bow for recruiting purposes at least. You're going to need some more patience otherwise, I'm sorry to say. Try the birds first-I got them all in a few tries-they're Friend Area is Legendary Island and they're at levels as follows:Zapados-Lvl 45, Moltres-Lvl 52, Articuno-Lvl 53-as long as your leader is a higher level you should be able to get them in 2 or 3 tries each, I think that's all that took me to get those birds, but that's a start! Good luck and don't take it so hard if you can't recruit them all easily-they had to make something in the game tough-give it more time and preparation at least!! I'm sure you're an excellent player-don't be so hard on yourself! I doubt I could go recruit him now myself, but I'll try and let you know if I do so easily, which I highly doubt! Oh, and you need Sacred Field friend area to get any of the doggies, too! Hang in there, don't get too frustrated, OK!

Yea so it's preety simple recruiting him friend arnea,friend bow,and a decent level like say aroud 50 or 60 but sometimes level dosent really matter I recruited the birds and I ws just lvl 38 with my mudkip for zapdos and following so hope I helped