  We develop a novel and unifying setting for phase retrieval problems that
works in Banach spaces and for continuous frames and consider the questions of
uniqueness and stability of the reconstruction from phaseless measurements. Our
main result states that also in this framework, the problem of phase retrieval
is never uniformly stable in infinite dimensions. On the other hand, we show
weak stability of the problem. This complements recent work [9], where it has
been shown that phase retrieval is always unstable for the setting of discrete
frames in Hilbert spaces. In particular, our result implies that the stability
properties cannot be improved by oversampling the underlying discrete frame.
  We generalize the notion of complement property (CP) to the setting of
continuous frames for Banach spaces (over $\mathbb{K}=\mathbb{R}$ or
$\mathbb{K}=\mathbb{C}$) and verify that it is a necessary condition for
uniqueness of the phase retrieval problem; when $\mathbb{K}=\mathbb{R}$ the CP
is also sufficient for uniqueness. In our general setting, we also prove a
conjecture posed by Bandeira et al. [5], which was originally formulated for
finite-dimensional spaces: for the case $\mathbb{K}=\mathbb{C}$ the strong
complement property (SCP) is a necessary condition for stability. To prove our
main result, we show that the SCP can never hold for frames of
infinite-dimensional Banach spaces.
