IIRC Almost the entire East Coast of the US was hit with some brutal weather the weekend that Avatar opened, which may have contributed to its' extremely strong second weekend showings vs. a larger opening weekend w/ a bigger second weekend drop, but there's no denying it had phenomenal staying power.
For those rooting for it to claim a top spot, Avengers has the disadvantage of being released at the beginning of the summer, when there's a lot more competition for viewers' dollars over the next few months. Avatar was basically competing with the usual crop of prestige pics upon opening and then pretty much had free reign for January and February. Doesn't mean its' staying power was anything less than amazing in the current cinema environment, but by comparison there's a heck of a lot more competition waiting in the wings for Avengers...maybe not so much in May, but certainly once June hits.
Titanic's staying power is somewhat less anomalous. It was a much different moviegoing (and more importantly home viewing) environment back then.
And Avengers has the disadvantage of not engaging in the female audience like I said before. That's what made Titanic and Avatar so huge is the universal appeal. Titanic staying power is somewhat less anomalous? The re-issue in 3D release this year grossed over 300M and it still going.