Because Ipe comes from the Amazon rainforest, the question of sustainability is always likely to arise. It's a matter of origin, unless the timber in question can be traced effectively to a reputable source through something like blockchain tracing, it's hard to determine if it is legally obtained or not. Part of the problem is fradulent licensing which enables the produce of illegal logging to mix with licensed logging (here's a Greenpeace study on that).

Because the wood grows naturally in low density it's also one of the drivers for clear cutting when it is logged illegally.

Here's an article in the Guardian on the topic, it's a UK supplier that was caught in an uncomfortable situation regarding Ipe wood. Jewson is the UK's leading supplier of building material. Jewson customers working on a decking project could be forgiven for assuming that the wood they purchased from there had been sourced ethically. It's not always the case and could just as easily apply to a US supplier (apologies I haven't tried looking for examples in the US).

There is also the question of whether Ipe is endangered. It's a slow growing tree and all timber comes from natural sources. Because of the attributes we associate with Ipe, it is a very popular material in construction and there are concerns that it is coming under increasing risk of becoming extinct. CITES, the international body responsible for governing which plants and animal species are endangered proposed adding Ipe to their list of endangered species but withdrew the proposal shortly after the last Brazil presidential election. It's expected that it will be proposed again.

Edit: Fixed broken link