I've noticed that the Q400 sometimes has difficulty flying arrivals which are designated RNP, showing similar altitude problems to what you describe. The few RNAV RNP arrivals I have attempted suffered from the aircraft being too high crossing some way points and experiencing difficulty when transitioning from the arrival to the approach. Setting the RNP in the FMC (shown on the chart) helps a bit. Mostly if I can fly the arrival, using a combination of VNAV/LNAV or VS, the aircraft will usually fly the RNP approach in VNAV ok. As I said, my Q400 struggles with the RNP arrivals.
Did the first poster have the Alt Sel set to a lower altitude? Alt Sel needs to be set lower than the cruise or present alt in order for the aircraft to descend.
I have since decided not to use any charts designated RNP and only use RNAV/GNSS or ILS charts, which work mostly perfectly in my q400 FMC. Using these arrivals & approaches I can't remember having a problem. Just keep an eye on the MDA, if using RNAV, and let the AP fly, or use the ILS