They are still wealthy, here is an up-to-date business insider article on Rothschild's descendents.
The reason they are not on the Forbe's list is because their wealth is diluted amongst many people; Forbes makes an effort to focus on individual wealth. Here's is a comment by Forbes employee Luisa Kroll:
Thanks for your note. The Rothschilds are a large, wealthy family, and
as you say, have accumulated their fortunes since the 1800s (FIXES
TYPO: I originally wrote 1980s. The family has been involved in
business for more than a century). Years ago when the number of
billionaires start to soar, we made the decision to focus on
individual wealth. We list brothers together, only if they are worth
an estimated $1 billion apiece or $2 billion-plus total. We list a
man, with his wife and children, if he’s the founder who built the
fortune, even if he’s passed on some shares. But otherwise we really
try to keep it focused on individuals. (Those fortunes with some
nuclear family sharing are denoted with & family). That is why the
family is not on, but Nat Rothschild, who has a personal fortune we
can trace, is among the 1,226 billionaires.
She makes another comment here:
Hi Luis, Thanks for your question. We used to have the Rothschild
family among the ranks but about a decade ago when we started to list
all billionaires in the world together (we used to list usa
separately), we decided to focus on individual wealth as best we
could. we thought it was a more apples to apples comparison, ranking
one entrepreneur versus 20 member family seemed not right, and also to
keep the list exclusive. We have not been able to pin down one
individual yet though the family are billionaires. We had Nat on our
list but he fell off after debacle in Indonesia. We’re looking closely
at Jacob and got him about half way there. If there are particular
individuals on whom you have info, please send. Otherwise, we’ll
continue to look for individual fortunes within large familes – they
are there but not always as easy to prove or break down.
As a side note, dilution of wealth amongst many progeny was a major concern of the original Rothschild who barred female descendents from receiving inheritance in an effort to ensure that the family's wealth remains concentrated.
But why are they not richer given that they had many years to accumulate their wealth? I think that there are a few possible reasons:
1) High inheritance taxes and capital gains taxes
2) Earning a higher return with a large amount of money is difficult. In his early days, Warren Buffett was able to return in excess of 25%. But as of 2013, his company has only returned 5.3% p.a..
3) Lower returns combined with yearly inflation may drastically reduce the rate of wealth accumulation
4) The Nazis confiscated a lot of their wealth, including their bank (and also forced them to flee Europe).