If the gate is fully driven to ground (or max rated Vgs)
then it must be a MOSFET on-resistance vs load current
problem. But you'd have to inspect for that to be sure.
If so, then spec a MOSFET whose RON at your load current
gives you less than the max allowed voltage drop.
Seeing "MOSFET-P" as the device callout makes me think
you are using a small-signal MOSFET where a proper
power MOSFET is really wanted. Go to IR's website and
pick off one you like the looks of.