Batteries not supplying enough voltage in DC motor circuit
Battery ESR

There is a relationship between Ah capacity of a battery and it's ESR.  


For a 6V SLA , it's about ESR= Ah/0.1 and for Li-Ion , ESR ~ Ah/50 but is more dependent on C rate.  It also adds with number of cells in series and divides by strings in parallel,


FET RdsOn

YOUR FET is rated at 8.7mΩ @ Vgs=10V and Vgs(th) 1.35 to 2.35 V only conducts 25uA so at 2.5Vdc it's probably &lt; 50 Ohms so your battery has high ESR.



MOTOR DCR

Your Motor also has DC resistance or DCR which you can measure with a DMM. 

This causes a surge current of V+/DCR which normally reduces to 10% at its rated load and 1% at no load.

Voltage drop

Ohm's Law...







simulate this circuit &ndash; Schematic created using CircuitLab

Need I say more?

Battery DCR rises with age and State of Discharge (SoD) rapidly &lt; 10% from sulphation or electrode oxidation etc.