I think the big unknown here is how much they'll start to dissimulate and/or offshore their (new) wealth.
According to one paper:
A recent study by Brülhart et al. (2017) gives support to the plausible assumption that the
effect of net wealth taxes on reported wealth is the more pronounced the more integrated
the regions involved are. According to the authors’ estimations, the semi-elasticity of
reported wealth with respect to the net wealth tax rate amounts to 35% in aggregate, i.e. a
rise in wealth taxation by one percentage point decreases reported wealth by 35%.
Moreover, Brülhart et al. (2017) find that financial assets seem to be more responsive to
taxation than non-financial assets. They also interpret their results as suggesting that
wealth holders primarily respond by reducing their wealth holdings, not by moving to
jurisdictions with lower tax rates.
So if that is true, then >3% wealth tax will result in "over" 100% dissimulation of new wealth. But caveat emptor, that's based on the fairly secretive Swiss:
It must be noted, however, that these analyses do not uncover the channels via which
wealth holdings are lowered. As indicated above, reported wealth holdings may be reduced
by real responses (i.e. by lowering accumulation of wealth) or by decreasing reported
wealth through hiding it from tax authorities. Which of these mechanisms is working in the
Swiss case cannot be determined without further analysis, e.g. by exploring whether there
is some relationship between the savings rate and the taxation of net wealth.
The biggest issue with extrapolating much from the Swiss case is that
Wealth taxes are cantonal and municipal; there is no federal taxation of wealth.
It's basically unknown how big that semi-elasticity would be if a whole country (like the US) had a wealth tax. France apparently had one, but it looks like they don't have a clear figure of the aforementioned elasticity, despite the fact that the rate changed a few times. It is known however that for about a decade there was a net outflow of around 300-500 people (per year) who would have qualified for the wealth tax, although they could have left for other reasons (including other parts of the tax code). France being in the EU also offers some special circumstances to migrate to neighboring countries but still (partly) invest in France.
If we ignore the potential flight or dissimulation, there's still the issue that billionaire wealth might decrease even in not so bad times, e.g.
Billionaires around the world saw their total wealth decline by 7% from 2017 to 2018, according to Wealth X’s Billionaire Census 2019. At the same time, the number of these ultra-high-net-worth individuals fell from 2,754 to 2,064.
American billionaires had an easier time.
The U.S. was one of the few countries that saw its UHNW population grow from 2017 to 2018, per the report, and America’s richest people lost only around 5% of their total wealth, far less than their peers did in most other regions. [...] Total U.S. billionaire wealth fell from \$3.2 trillion to \$3.013 trillion.
So, before we talk of sustainability, we'd need to decide on some time frame. Clearly their (total) wealth can go down year-to-year even with no wealth tax, although the trade war was apparently blamed for the recent downward trend. From 2015 to 2016 it actually went up 15%.
In 2016, US billionaires saw their wealth increase from USD 2.4 trillion to USD 2.8 trillion
So it looks like US billionaire wealth is more volatile than the US economy as a whole.