personally, i use palringo, and it works incredibly well. i dont see any issues like u mentioned ( i still recive messages even is my screen is off) and it supports most major services and have alot of handy features.
I love the voice chat option, sometimes you cant type so u can send a little prerecorded message and the other end recives a link to play. and sending pics is a breeze.
try it out. Hope that helps.
http://www.palringo.com/en/gb/
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Good Luck and Happy Modding.
I love: Swype, Pandora, AmonRa Recovery and Touiteur.
I hate: Swype (haha), 4G dropping constantly, screen protectors and losing signal in the DC subways