The spin injection dynamics of GaMnN/InGaN multiquantum well (MQW) light emitting diodes (LEDs) grown by molecular beam epitaxy were examined using picosecond-transient and circularly polarized photoluminescence (PL) measurements. Even with the presence of a room temperature ferromagnetic GaMnN spin injector, the LEDs are shown to exhibit very low efficiency of spin injection. Based on resonant optical orientation spectroscopy, the spin loss in the structures is shown to be largely due to fast spin relaxation within the InGaN MQW, which itself destroys any spin polarization generated by optical spin orientation or electrical spin injection. Typical photoluminescence decay times were 20-40 ns in both commercial GaN MQW LEDs with emission wavelengths between 420-470 nm and in the GaMnN/InGaN multi-quantum well MQW LEDs. In the wurtzite InGaN/GaN system, biaxial strain at the interfaces give rise to large piezoelectric fields directed along the growth axis. This built-in piezofield breaks the reflection symmetry of confining potential leading to the presence of a large Rashba term in the conduction band Hamiltonian which is responsible for the short spin relaxation times.