The motor would perform better with a pure DC supply - a battery or well-smoothed DC source - but not at the expense of raising the voltage beyond the design level. This will cause other problems.
Don't forget that the relays switch a lot of current when the motor is at standstill because there is no back EMF from the armature. If the motor is separately excited or has a shunt field, there will be a powerful inductive arc at switch-off caused by the energy stored in the field circuit which will burn relay pole faces.
You say 'relays' rather than 'contactor'. For this sort of duty it would be normal to spec a contactor rather than a relay. In Europe at least, 120V DC is a fairly common control voltage and contactors are available suited to motor switching duty. If this is an industrial application look for DC3 duty contactors or maybe DC5 duty if the motor is particularly inductive.
On re-reading your post, I have assumed that the relays are failing through contact damage, not coil failure. Have I mis-assumed?
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