I guess chipmixer is going to stay, but why? And this "why" isn't simple question.
Probably because it's not doing anything illegal:
A mixing service will cut up a sum of Bitcoins into hundreds of smaller transactions and mixes different transactions from other sources for obfuscation and will pump out the input amount, minus a fee, to a certain output address. Mixing Bitcoins that are obtained legally is not a crime but, other than the mathematical exercise, there no real benefit to it.
The legality changes when a mixing service advertises itself as a success method to avoid various anti-money laundering policies via anonymity. This is actively offering a money laundering service.
[...]
Bestmixer offered a very clear page on why someone should mix their cryptocurrency. On this page Bestmixer described the current anti-money laundering policies and how its service could help evade these policies by making funds anonymous and untraceable. Offering such a service is considered illegal in many countries.
McAfee was involved in this case, so I can only assume that this was the real (official, at least) reason for Bestmixer's shutdown. If you don't want to open the linked article, it shows that Bestmixer had a page that basically tells you you can avoid anti-money laundering policies with its service. Chipmixer has nothing to worry about if this is the case.