  One of the great challenges of quantum foundations and quantum information
theory is the characterisation of the relationship between entanglement and the
violation of Bell inequalities. It is well known that in specific scenarios
these two can behave differently, from local hidden-variable models for
entangled quantum states in restricted Bell scenarios, to maximal violations of
Bell inequalities not concurring with maximal entanglement. In this paper we
put forward a simple proof that there exist quantum states, whose entanglement
content, as measured by the Schmidt number, cannot be device-independently
certified for all possible sequential measurements on any number of copies.
While the bigger question: \textit{can the presence of entanglement always be
device-independently certified?} remains open, we provide proof that
quantifying entanglement device-independently is not always possible, even
beyond the standard Bell scenario.
