Though the story never does mention "constant feasts and parties," since Prince Prospero had provided his "castellated" abbey with all good things, including wine and entertainers, it must be supposed that the revelers ate and drank in abundance. Rewriting your question a bit, it is appropriate to ask about the reason for the revelers' assumed feasts and gayeties: Why is there feasting in the story?
The abbey was amply provisioned. With such precautions the courtiers might bid defiance to contagion. The external world could take care of itself. In the meantime it was folly to grieve, or to think. The prince had provided all the appliances of pleasure. There were buffoons, there were improvisatori, there were ballet-dancers, there were musicians, there was Beauty, there was wine. All these and security were within.
Bear in mind that "The Mask of the Red Death" is ultimately analyzed as an allegory for the struggle of the artist to put a spatial limit on temporal reality: An attempt to confine the life-to-death temporal (time-centered) experience of artists to a transcendent spatial existence--with words and canvases that live on--is doomed to failure because death and decay await the artist, always rendering his task incomplete and unfulfilled. With this in mind, the symbolic purpose of the feasting can easily fit into the allegory of the artist struggling against the conflict between time and space, temporality and spatiality.
If Prospero is Poe's allegorical representation of the Artist, and if the rooms represent the Time journey through life from birth to death, and if the guests are allegorical representations of other artists or artists' admirers, then the feasting is the celebration of the productivety and of the talent, gift, resources of the artist who captures Art in configurations in Space (words, paintings, statues, clocks etc). The symbolic feasting in the allegory represents the impact of the artist's benefactions of great and inspiring works of art given to humanity and the joyful celebratory actions with which the gifts of art are received.
In a different analysis in which the central point of the Gothic tale is the horror of preserving life in the pervading face of inevitable Death, the symbolic feasts may be said to represent the blind frivolity with which life is carried on in joyous style having little regard to the seriousness of the encroaching power of Death to still all activity, leaving serious tasks unattended to as Time is consumed as one greedily consumes food at feasts.