Is there enough information given to solve the problem? You list a maximum rate of H2 consumption (200 g/hr). Is that close to the typical flow rate? Or are you considering a "worst case" scenario (how long will the H2 last at the maximum flow rate?)?
As phrased, you are asking about calculating how quickly the pressure drops -- you want to find dP/dt. Could you do something like:
Choose your favorite EOS for H2. P=f(T,V,m)
from EOS, you should be able to determine dP/dm
take your given typical or maximum (or other desired) mass flow rate -- dm/dt
Chain rule should allow you to compute the rate of change for the pressure dP/dt=dP/dm*dm/dt
Integrate dP/dt between Pmax and Pmin to get total time.
If I were looking at this problem, I would wonder if the rate of change in pressure is really that important. I might solve the problem like this:
From EOS, compute m H2 at max P, T, and V
From EOS, compute m H2 at min P, T, and V
The difference of those two is the mass of H2 available to the reactor
from typical or maximum or other mass flow rate, determine time needed to consume the available mass of H2. This computation would usually assume that dm/dt is constant, independent of pressure (only you would know if that is a good assumption). If that is a good assumption, then this is probably simpler than the previous.