This paper studies the question whether automated market maker protocols such as Uniswap can sustainably retain a portion of their trading fees for the protocol. We approach the problem by modelling how to optimally choose a pool's take rate, i.e\ the fraction of fee revenue that remains with the protocol, in order to maximize the protocol's revenue. The model suggest that if AMMs have a portion of loyal trade volume, they can sustainably set a non-zero take rate, even without losing liquidity to competitors with a zero take rate. Furthermore, we determine the optimal take rate depending on a number of model parameters including how much loyal trade volume pools have and how high the competitors' take rates are.