Can somebody please help out a Big Bang Theory fan?

In sitcom लेखन character development tends to be limited, usually द्वारा the end of an episode everything is returned to how it was in the beginning.
In particular with Raj, his inability to chat up girls is his essential idiosyncrasy, without it he wouldn't be half as nerdy as the other guys, all of whom have issues with the opposite gender (or in Sheldon's case, other people in general.)
That isn't to say that he couldn't ever overcome his debilitating shyness, I just couldn't foresee such a thing happening without it being a majorly Raj-focused storyline या arc.
In any event, IMO to alleviate such a defining characteristic so early in the series seems inadvisable as it is a स्रोत of quite a bit of the Raj-oriented humor.

Your wording of "it annoys me because one episode he does and the अगला he doesn't" sounds like it's a writer flaw - at least to me - and it's not. They've been really consistant with it - he has to be drunk (or distracted, 1.13) to really be able to talk. So technically they did "stick with it". After that episode he is consistant in talking to them when drunk. :)