  Current terrestrial gravitational-wave detectors operate at frequencies above
10 Hz. There is strong astrophysical motivation to construct low-frequency
gravitational-wave detectors capable of observing 10 mHz - 10Hz signals. While
space-based detectors provide one means of achieving this end, one may also
consider terretrial detectors. However, there are numerous technological
challenges. In particular, it is difficult to isolate test masses so that they
are both seismically isolated and freely falling under the influence of gravity
at millihertz frequencies. We investigate the challenges of low-frequency
suspension in a hypothetical terrestrial detector. As a case study, we consider
a Magnetically Assisted Gravitational-wave Pendulum Intorsion (MAGPI)
suspension design. We construct a noise budget to estimate some of the required
specifications. In doing so, we identify what are likely to be a number of
generic limiting noise sources for terrestrial millihertz gravitational-wave
suspension systems (as well as some peculiar to the MAGPI design). We highlight
significant experimental challenges in order to argue that the development of
millihertz suspensions will be a daunting task. Any system that relies on
magnets faces even greater challenges. Entirely mechanical designs such as
Zollner pendulums may provide the best path forward.
